CMU logic events during coming week
Mathematical logic seminar: 3:30 P.M., Online, James Cummings, Carnegie Mellon University
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: Homological algebra for logicians
ABSTRACT: This is part 3 of a short series of talks aimed at giving some background for Nathaniel Bannister's forthcoming seminars. Nathaniel's talks will describe his work with Bergfalk and Moore on the additivity of strong homology.
I will give a rapid overview of some necessary background in homological algebra (eg abelian categories, chain complexes, derived functors). I will assume very little background, just familiarity with basic notions in category theory (category, functor, natural transformation) and algebra (the definition of an R-module).
TUESDAY, June 15, 2021
Set Theory Reading Group: 4:30 P.M., Online, James Cummings, Carnegie Mellon University
Join Zoom Meeting: https://cmu.zoom.us/j/621951121 [cmu.zoom.us]
Meeting ID: 621 951 121
TITLE: Homological algebra for logicians
ABSTRACT: This is part 4 of a short series of talks aimed at giving some background for Nathaniel Bannister's forthcoming seminars. Nathaniel's talks will describe his work with Bergfalk and Moore on the additivity of strong homology.
I will give a rapid overview of some necessary background in homological algebra (eg abelian categories, chain complexes, derived functors). I will assume very little background, just familiarity with basic notions in category theory (category, functor, natural transformation) and algebra (the definition of an R-module).
THURSDAY, June 17, 2021
Ph.D. Thesis Defense: 12:00 P.M., Online, Marcos Mazari-Armida
Zoom:
https://cmu.zoom.us/j/96301869290?pwd=Qk1zS0h6ZThmUnRpbmNLNkVJSjkrQT09
TITLE OF DISSERTATION: Remarks on classification theory for abstract elementary classes with applications to abelian group theory and ring theory
EXAMINERS:
Prof. Rami Grossberg (Committee Chair)
Prof. Jeremy Avigad
Prof. John Baldwin, UIC
Prof. Will Boney, Texas State
Prof. James Cummings
Barcelona Set theory Seminar
Talk tomorrow by Piotr Szewczak (1:30 pm Toronto time)
Talk this Friday June 4th by Piotr Szewczak (1:30 pm Toronto time)
Barcelona Set theory Seminar
Two events on June 8
Talk Tomorrow by Boban Velickovic at 1 30 (Toronto time)
(KGRC) research seminar talk on Thursday, May 27
An interesting series of talks for grad students
introduce some areas of set theory to the students.
them to the list of participants. vera.fischer@univie.ac.at
(it is 9:30am CET, Fridays, May 28-June 18), but she will record the
talks for those who want to hear them at a later point. Here is
the program until the end of the semester.
https://sites.google.com/view/short-talks-logic-uni-wien/home
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Talk Friday May 27th (this friday) by Boban Velickovic at 1 30 (Toronto time)
Barcelona Set theory Seminar
Barcelona Set theory Seminar
Barcelona Set theory Seminar
(KGRC) research seminar talk on Thursday, May 20
Barcelona Set theory Seminar
This Week in Logic at CUNY
- - - - Monday, May 3, 2021 - - - -
Date: Monday, May 3rd, 4.15-6.15 (NY time)
Title: Marsilius of Inghen, John Buridan and the Semantics of Impossibility
Abstract: In the 14th-century, imaginable yet in some sense impossible non-entities start playing a crucial role in logic, natural philosophy and metaphysics. Throughout the later middle ages and well into early modernity, Marsilius of Inghen’s name comes to be unavoidably associated with the semantics of imaginable impossibilities in most logical and metaphysical discussions. In this paper I analyse Marsilius of Inghen’s semantic treatment of impossible referents, through a comparison with John Buridan’s. While in many ways Marsilius is profoundly influenced by Buridan’s philosophy, his semantic analysis of impossibilia is radically different from Buridan’s. Overall, Buridan tends to analyse away impossible referents in terms of complex concepts by combining possible simple individual parts. Marsilius, on the one hand, treats impossibilia as imaginable referents that are properly unitary; on the other hand, he extends the scope of his modal semantics beyond the inclusion of merely relative impossibilities, allowing for a full semantic treatment of absolute impossibilities as well. Here, I will explore the extent of these differences between Buridan’s and Marsilius of Inghen’s semantics, their presuppositions, and their respective conceptual impact on early modern philosophy of logic and mathematics.
- - - - Tuesday, May 4, 2021 - - - -
- - - - Wednesday, May 5, 2021 - - - -
- - - - Thursday, May 6, 2021 - - - -
Philog Seminar
CUNY Graduate Center
Thursday May 6, 2021, 6:30 PM
Ada Coronado
Nietzsche on, Logic, Philosophy, and Moral Values
Introduction: Studies in logic rarely ever mention Fredrich Nietzsche. There is very little literature on Nietzsche’s critique of classical logic and there is no indication that he followed the developments that were occurring in the field in the 19th century by contemporaneous thinkers such as George Boole, Frege, or Augustus De Morgan. Yet, logic is central to Nietzsche’s seminal work Beyond Good and Evil: Prelude to a Philosophy of the Future, henceforth referred to as BGE. Believing that classical logic falsely reinforces the religious promise of absolutism and certainty, Nietzsche rejects the possibility of a priori truths qua truth, but embraces logic to the extent that he considers it the vehicle that systematically discharges a philosopher’s energy and morality onto the world.
In this talk I consider Nietzsche’s critique of moral values as they relate to his rejection of both a priori truths and the semantic principle of bivalence, or what he calls the “faith of opposite values”. I argue that Nietzsche’s approach to philosophy, logic, and moral values heralds the future philosophical significance of multivalent systems and paraconsistent logic.
A Zoom link will be posted on https://philog.arthurpaulpedersen.org/
- - - - Friday, May 7, 2021 - - - -
This oral exam talk will present a proof of Woodin's result that every real number is generic over some iterated ultrapower of any model with a Woodin cardinal. No fine structure theory will be used, and there will be a brief introduction to iteration trees.
Next Week in Logic at CUNY:
- - - - Monday, May 10, 2021 - - - -
Date: Monday, May 10th, 4.15-6.15 (NY time)
Title: Heidegger on the Limits and Possibilities of Human Thinking
Abstract: In my talk, I will address what Heidegger calls ‘the basic problem’ of his philosophy, that is, the alleged incompatibility between the notion of Being, our thinking, and logic. First of all, I will discuss some of the ways in which Heideggerians have dealt with this incompatibility by distinguishing what I call the irrationalist and rationalist interpretation. Secondly, I will argue that these two interpretations face both exegetical and philosophical problems. To conclude, I will defend an alternative way to address the incompatibility between the notion of Being, our thinking, and logic. I will argue that, in some of his late works, Heidegger seems to suggest that the real problem lies in the philosophical illusion that we can actually assess the limits of our thinking and, therewith, our logic. Heidegger’s philosophy, I deem, wants to free us from such a philosophical illusion by delivering an experience which reminds us that our thinking is something we can never ‘look at from above’ in order to either grasp its limits or realize that it has no limits whatsoever.
- - - - Tuesday, May 11, 2021 - - - -
- - - - Wednesday, May 12, 2021 - - - -
- - - - Thursday, May 13, 2021 - - - -
Philog Seminar
CUNY Graduate Center
Thursday May 13, 2021, 6:30 PM
Eric Pacuit, University of Maryland
- - - - Friday, May 14, 2021 - - - -
Maximal almost disjoint (MAD) families and their relatives have been an important area of combinatorial and descriptive set theory since at least the 60s. In this talk I will discuss some relatives of MAD families, focussing on eventually different families of functions f:ω→ω and eventually different sets of permutations p∈S(ω). In the context of MAD families it has been fruitful to consider various strengthenings of the maximality condition to obtain several flavors of 'strongly' MAD families. One such strengthening that has proved useful in recent literature is that of tightness. Tight MAD families are Cohen indestructible and come with a properness preservation theorem making them nice to work with in iterated forcing contexts.
I will introduce a version of tightness for maximal eventually different families of functions f:ω→ω and maximal eventually different families of permutations p∈S(ω) respectively. These tight eventually different families share a lot of the nice, forcing theoretic properties of tight MAD families. Using them, I will construct explicit witnesses to ae=ap=ℵ1 in many known models of set theory where this equality was either not known or only known by less constructive means. Working over L we can moreover have the witnesses be Π11 which is optimal for objects of size ℵ1 in models where CH fails. These results simultaneously strengthen several known results on the existence of definable maximal sets of reals which are indestructible for various definable forcing notions. This is joint work with Vera Fischer.
- - - - Monday, May 17, 2021 - - - -
- - - - Tuesday, May 18, 2021 - - - -
- - - - Wednesday, May 19, 2021 - - - -
- - - - Thursday, May 20, 2021 - - - -
- - - - Friday, May 21, 2021 - - - -
- - - - Web Site - - - -
"Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)"
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Barcelona Set theory Seminar
All links to today talk work (preferably, use the one to fill the form)
Today (Friday, 7th) talk by Itsvan Juhasz
Talk Tomorrow by Itsvan Juhasz at 1 30 pm (Toronto time)
Topic: Set Theory Seminar
Time: 1:30-3:00 pm Friday May 7th
Join Zoom Meeting
https://zoom.us/j/97109130026?pwd=a2VMVUJBMmZweXU4a0ZnaE02NmJvZz09
Meeting ID: 971 0913 0026
Passcode: 729463
One tap mobile
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Dial by your location
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Meeting ID: 971 0913 0026
Find your local number: https://zoom.us/u/abXb8IbMLt
Hello everyone,Please use the following link and fill the form (every week) to enter the meeting. This form helps the Field Institute to know statistical data about attendance.Here the speaker information:Speaker: Itsvan JuhaszDate and Time: Friday, May 7th, 2021 - 1:30pm to 3:00pmTitle: Anti-Urysohn spacesAbstract: please see attached pdf or visit http://www.fields.utoronto.ca/talks/Anti-Urysohn-spacesIván Ongay Valverde (he/his)My email account ongay@math.wisc.edu will be closed in October 2020. Please contact me either at ongay@yorku.ca or at ivan.ongay.valverde@gmail.com
Talk Tomorrow by Itsvan Juhasz at 1 30 pm (Toronto time)
This Week in Logic at CUNY
- - - - Monday, May 3, 2021 - - - -
Date: Monday, May 3rd, 4.15-6.15 (NY time)
Title: Marsilius of Inghen, John Buridan and the Semantics of Impossibility
Abstract: In the 14th-century, imaginable yet in some sense impossible non-entities start playing a crucial role in logic, natural philosophy and metaphysics. Throughout the later middle ages and well into early modernity, Marsilius of Inghen’s name comes to be unavoidably associated with the semantics of imaginable impossibilities in most logical and metaphysical discussions. In this paper I analyse Marsilius of Inghen’s semantic treatment of impossible referents, through a comparison with John Buridan’s. While in many ways Marsilius is profoundly influenced by Buridan’s philosophy, his semantic analysis of impossibilia is radically different from Buridan’s. Overall, Buridan tends to analyse away impossible referents in terms of complex concepts by combining possible simple individual parts. Marsilius, on the one hand, treats impossibilia as imaginable referents that are properly unitary; on the other hand, he extends the scope of his modal semantics beyond the inclusion of merely relative impossibilities, allowing for a full semantic treatment of absolute impossibilities as well. Here, I will explore the extent of these differences between Buridan’s and Marsilius of Inghen’s semantics, their presuppositions, and their respective conceptual impact on early modern philosophy of logic and mathematics.
- - - - Tuesday, May 4, 2021 - - - -
- - - - Wednesday, May 5, 2021 - - - -
- - - - Thursday, May 6, 2021 - - - -
Philog Seminar
CUNY Graduate Center
Thursday May 6, 2021, 6:30 PM
Ada Coronado
Nietzsche on, Logic, Philosophy, and Moral Values
Introduction: Studies in logic rarely ever mention Fredrich Nietzsche. There is very little literature on Nietzsche’s critique of classical logic and there is no indication that he followed the developments that were occurring in the field in the 19th century by contemporaneous thinkers such as George Boole, Frege, or Augustus De Morgan. Yet, logic is central to Nietzsche’s seminal work Beyond Good and Evil: Prelude to a Philosophy of the Future, henceforth referred to as BGE. Believing that classical logic falsely reinforces the religious promise of absolutism and certainty, Nietzsche rejects the possibility of a priori truths qua truth, but embraces logic to the extent that he considers it the vehicle that systematically discharges a philosopher’s energy and morality onto the world.
In this talk I consider Nietzsche’s critique of moral values as they relate to his rejection of both a priori truths and the semantic principle of bivalence, or what he calls the “faith of opposite values”. I argue that Nietzsche’s approach to philosophy, logic, and moral values heralds the future philosophical significance of multivalent systems and paraconsistent logic.
A Zoom link will be posted on https://philog.arthurpaulpedersen.org/
- - - - Friday, May 7, 2021 - - - -
This oral exam talk will present a proof of Woodin's result that every real number is generic over some iterated ultrapower of any model with a Woodin cardinal. No fine structure theory will be used, and there will be a brief introduction to iteration trees.
Next Week in Logic at CUNY:
- - - - Monday, May 10, 2021 - - - -
Date: Monday, May 10th, 4.15-6.15 (NY time)
Title: Heidegger on the Limits and Possibilities of Human Thinking
Abstract: In my talk, I will address what Heidegger calls ‘the basic problem’ of his philosophy, that is, the alleged incompatibility between the notion of Being, our thinking, and logic. First of all, I will discuss some of the ways in which Heideggerians have dealt with this incompatibility by distinguishing what I call the irrationalist and rationalist interpretation. Secondly, I will argue that these two interpretations face both exegetical and philosophical problems. To conclude, I will defend an alternative way to address the incompatibility between the notion of Being, our thinking, and logic. I will argue that, in some of his late works, Heidegger seems to suggest that the real problem lies in the philosophical illusion that we can actually assess the limits of our thinking and, therewith, our logic. Heidegger’s philosophy, I deem, wants to free us from such a philosophical illusion by delivering an experience which reminds us that our thinking is something we can never ‘look at from above’ in order to either grasp its limits or realize that it has no limits whatsoever.
- - - - Tuesday, May 11, 2021 - - - -
- - - - Wednesday, May 12, 2021 - - - -
- - - - Thursday, May 13, 2021 - - - -
- - - - Friday, May 14, 2021 - - - -
- - - - Web Site - - - -
"Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)"
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
(KGRC) research seminar talk on Thursday, May 6
(KGRC) research seminar talk on Thursday, April 29
This Week in Logic at CUNY
- - - - Monday, Apr 26, 2021 - - - -
Date: Monday, April 26th, 4.15-6.15 (NY time)
Title: Non-Classical Metatheory
Abstract: A common line of thinking has it that proponents of non-classical logics who claim that their preferred logic L gives the correct account of validity, while at the same time giving proofs of theorems about L using classical logic, are in some sense being insincere in their claim that L is the correct logic. This line of thought quite naturally motivates a correctness requirement on a non-classical logic L: that it be able to provide internally acceptable proofs of its main metatheorems. Of central importance amongst such metatheorems will typically be soundness and completeness results, such results being apt to play important roles in arguments showing that a given logic gives the correct account of validity. On the face of it this sounds like a reasonable requirement, but determining its precise content requires us to settle two important conceptual questions: what counts as a completeness proof for a logic, and what does it mean for a result to be internally acceptable? To get clearer on this issue we will look at three different results which have some claim to being internally acceptable soundness and completeness proofs, focusing for ease of comparison on the case of intuitionistic propositional logic, examining the extent to which they can be said to provide internally acceptable soundness and completeness results.
- - - - Tuesday, Apr 27, 2021 - - - -
Dave Marker, University of Illinois at Chicago
Real closures of ω1-like models of PA
D'Aquino, Knight and Starchenko showed the real closure of a model of Peano Arithmetic is recursively saturated. Thus any two countable models of PA with the same standard system have isomorphic real closures. Charlie Steinhorn, Jim Schmerl and I showed that even for ω1-like model of PA the situation is very different. We construct 2ℵ1 recursively saturated elementarily equivalent ω1-like models of PA with the same standard system and non-isomorphic real closures.
- - - - Thursday, Apr 29, 2021 - - - -
- - - - Friday, Apr 30, 2021 - - - -
Paradoxes of perfectly small sets
We define a set of real numbers to be perfectly small if it has perfectly many disjoint translates. Such sets have a strong intuitive claim to being probabilistically negligible, yet no non-trivial measure assigns them all a value of 0. We will prove from a moderate amount of choice that any total extension of Lebesgue measure concentrates on a perfectly small set, suggesting that for any such measure, translation-invariance fails 'as badly as possible.' From the ideas of this proof, we will also derive analogues of well-known paradoxes of randomness, specifically Freiling's symmetry paradox and the infinite prisoner hat puzzle, in terms of perfectly small sets. Finally, we discuss how these results constrain what a paradox-free set theory can look like and some related open questions.
- - - - Monday, May 3, 2021 - - - -
Date: Monday, May 3rd, 4.15-6.15 (NY time)
Title: Marsilius of Inghen, John Buridan and the Semantics of Impossibility
Abstract: In the 14th-century, imaginable yet in some sense impossible non-entities start playing a crucial role in logic, natural philosophy and metaphysics. Throughout the later middle ages and well into early modernity, Marsilius of Inghen’s name comes to be unavoidably associated with the semantics of imaginable impossibilities in most logical and metaphysical discussions. In this paper I analyse Marsilius of Inghen’s semantic treatment of impossible referents, through a comparison with John Buridan’s. While in many ways Marsilius is profoundly influenced by Buridan’s philosophy, his semantic analysis of impossibilia is radically different from Buridan’s. Overall, Buridan tends to analyse away impossible referents in terms of complex concepts by combining possible simple individual parts. Marsilius, on the one hand, treats impossibilia as imaginable referents that are properly unitary; on the other hand, he extends the scope of his modal semantics beyond the inclusion of merely relative impossibilities, allowing for a full semantic treatment of absolute impossibilities as well. Here, I will explore the extent of these differences between Buridan’s and Marsilius of Inghen’s semantics, their presuppositions, and their respective conceptual impact on early modern philosophy of logic and mathematics.
- - - - Tuesday, May 4, 2021 - - - -
- - - - Wednesday, May 5, 2021 - - - -
- - - - Thursday, May 6, 2021 - - - -
- - - - Friday, May 7, 2021 - - - -
- - - - Web Site - - - -
"Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)"
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Barcelona Set theory Seminar
Two CMU events on Tuesday, April 27
(KGRC) research seminar talk on Thursday, April 22
This Week in Logic at CUNY
- - - - Monday, Apr 19, 2021 - - - -
Date: Monday, April 19th, 4.15-6.15 (NY time)
Title: Brouwer’s First Act of Intuitionism
Abstract: L.E.J. Brouwer famously argued that mathematics was completely separated from formal language. His explanation for why this is so leaves room for interpretation. Indeed, one might ask: what sort of philosophical background is required to make sense of the strong anti-linguistic views of Brouwer? In this talk, we outline some possible answers to the above. We then present an interpretation that we argue best makes sense of Brouwer’s first act.
- - - - Tuesday, Apr 20, 2021 - - - -
Induction and collection up to definable elements: calibrating the strength of parameter-free Δn-minimization.
In this talk we shall deal with fragments of first-order Peano Arithmetic obtained by restricting the conclusion of the induction or the collection axiom to elements in a prescribed subclass D of the universe. Fix n>0. The schemes of Σn-induction up to Σm-definable elements and the schemes of Σn-collection up to Σm-definable elements form two families of subtheories of IΣn and BΣn, respectively, obtained in this way.
The properties of Σn-induction up to Σm-definable elements for n≥m are reasonably well understood and interesting applications of these fragments are known. However, an analysis of the case n<m was pending. In the first part of this talk, we address this problem and show that it is related to the following general question: 'Under which conditions on a model M can we prove that every non-empty Σm-definable subset of M contains some Σm-definable element?'
In the second part of the talk, we show that, for each n≥1, the scheme of Σn-collection up to Σn-definable elements provides us with an axiomatization of the Σn+1-consequences of BΣn. As an application, we obtain that BΣn is Σn+1-conservative over parameter-free Δn-minimization (plus IΣn−1), thus partially answering a question of R. Kaye.
This is joint work with F.Félix Lara-Martín (University of Seville).
- - - - Wednesday, Apr 21, 2021 - - - -
- - - - Thursday, Apr 22, 2021 - - - -
Philog Seminar
Thursday, April 22, 2021, 6:30 PM
Todd Stambaugh (John Jay)
Knowledge, behavior, and rationality: Rationalizability in epistemic games
Abstract: In strategic situations, agents base actions on knowledge and beliefs. This includes knowledge about others’ strategies and preferences over strategy profiles, but also about other external factors. Bernheim and Pearce in 1984 independently defined the game theoretic solution concept of rationalizability, which is built on the premise that rational agents will only take actions that are the best response to some situation that they consider possible.
This accounts for other agents’ rationality as well, limiting the strategies to which a particular agent must respond, enabling further elimination until the strategies stabilize. We seek to generalize rationalizability to account not only for actions, but knowledge of the world as well. This will enable us to examine the interplay between action based and knowledge based rationality.
We give an account of what it means for an action to be rational relative to a particular state of affairs, and in turn relative to a state of knowledge. We present a class of games, Epistemic Messaging Games (EMG), with a communication stage that clarifies the epistemic state among the players prior to the players’ actions. We use a history based model, which frames individual knowledge in terms of local projections of a global history. With this framework, we give an account of rationalizability for subclasses of EMG
(Joint work with Rohit Parikh. Todd Stambaugh received his doctorate in 2018, from the mathematics program of CUNY).
A Zoom link will be posted on philog.arthurpaulpedersen.org on Wednesday
- - - - Friday, Apr 23, 2021 - - - -
Andrés Villaveces, Universidad Nacional de Colombia – Bogotá
Two logics, and their connections with large cardinals / Questions for BDGM: Part II
In the past couple of years I have been involved (joint work with Väänänen and independently with Shelah) with some logics in the vicinity of Shelah's L1κ (a logic from 2012 that has Interpolation and a very weak notion of compactness, namely Strong Undefinability of Well-Orderings, and in some cases has a Lindström-type theorem for those two properties). Our work with Väänänen weakens the logic but keeps several properties. Our work with Shelah explores the connection with definability of AECs.
These logics seem to have additional interesting properties under the further assumption of strong compactness of a cardinal, and this brings them close to recent work of Boney, Dimopoulos, Gitman and Magidor [BDGM].
During the first lecture, I plan to describe two games and a syntax of two logics: Shelah's L1κ and my own logic (joint work with Väänänen) L1,cκ. I will stress some of the properties of these logics, without any use of large cardinal assumptions.
During the second lecture, I plan to enter rather uncharted territory. I will describe some constructions done by Shelah (mostly) under the assumption of strong compactness, but I also plan to bring these logics to a territory closer to the work of [BDGM]. This second lecture will have more conjectures, ideas, and (hopefully interesting) discussions with some of the authors of that paper.
- - - - Monday, Apr 26, 2021 - - - -
Date: Monday, April 26th, 4.15-6.15 (NY time)
Title: Non-Classical Metatheory
Abstract: A common line of thinking has it that proponents of non-classical logics who claim that their preferred logic L gives the correct account of validity, while at the same time giving proofs of theorems about L using classical logic, are in some sense being insincere in their claim that L is the correct logic. This line of thought quite naturally motivates a correctness requirement on a non-classical logic L: that it be able to provide internally acceptable proofs of its main metatheorems. Of central importance amongst such metatheorems will typically be soundness and completeness results, such results being apt to play important roles in arguments showing that a given logic gives the correct account of validity. On the face of it this sounds like a reasonable requirement, but determining its precise content requires us to settle two important conceptual questions: what counts as a completeness proof for a logic, and what does it mean for a result to be internally acceptable? To get clearer on this issue we will look at three different results which have some claim to being internally acceptable soundness and completeness proofs, focusing for ease of comparison on the case of intuitionistic propositional logic, examining the extent to which they can be said to provide internally acceptable soundness and completeness results.
- - - - Tuesday, Apr 27, 2021 - - - -
Dave Marker, University of Illinois at Chicago
Real closures of ω1-like models of PA
D'Aquino, Knight and Starchenko showed the real closure of a model of Peano Arithmetic is recursively saturated. Thus any two countable models of PA with the same standard system have isomorphic real closures. Charlie Steinhorn, Jim Schmerl and I showed that even for ω1-like model of PA the situation is very different. We construct 2ℵ1 recursively saturated elementarily equivalent ω1-like models of PA with the same standard system and non-isomorphic real closures.
- - - - Thursday, Apr 29, 2021 - - - -
- - - - Friday, Apr 30, 2021 - - - -
- - - - Web Site - - - -
"Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)"
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Barcelona Set theory Seminar
Tomorrow talk by Micheal Hrusak (1:30 pm Toronto time)
families and ultrafilters using the Kat\v{e}tov order, concentrating on
open problems.
Friday 16th talk by Micheal Hrusak (1:30 pm Toronto time)
families and ultrafilters using the Kat\v{e}tov order, concentrating on
open problems.
(KGRC) research seminar talk on Thursday, April 15
Two talks on Tuesday, April 20
UPDATE: This Week in Logic at CUNY
Date: Monday, April 12th, 4.15-6.15 (NY time)
Abstract: Bolzano is famously responsible for an influential substitutional account of logical consequence (or, as he calls it, logical deducibility): a proposition, 𝜑, is logically deducible from a set of propositions, Γ, iff every uniform substitution of non-logical ideas in Γ∪{𝜑} that makes every proposition in Γ true also makes 𝜑 true. There are two problems with making sense of Bolzano’s proposal, however. One is that Bolzano argues that every proposition is of the form a has B—in other words, is a monadic atomic predication. So, for Bolzano, logically complex propositions like ‘𝜑 and 𝜓’ cannot have the semantic structure they appear to. This can be addressed, roughly, by taking complex propositions to predicate logical ideas of collections of propositions. But this introduces the second problem: for Bolzano, familiar logical ideas like ‘and’, ‘or’, and ‘not’ are complex ideas with compositional structure. I’ll show that, as a result of this structure, we cannot use the simple and familiar notion of uniform substitution in order to understand logical deducibility. We must instead use what I’ll call form-sensitive substitution. I will end by drawing some general lessons about substitutional definitions of logical consequence in languages with the resources to generate complex predicates of propositions.
- - - - Tuesday, Apr 13, 2021 - - - -
Roman Kossak, CUNY
Automorphisms, Jónsson Models, and Satisfaction Classes
25 years ago I wrote a paper on four open problems concerning recursively saturated models of PA. The problems are still open. I will talk about two of them: (1) Let M be a countable recursively saturated model of PA. Can every automorphism of M be extended to some recursively saturated elementary end extension of M? (2) Is there a recursively saturated model of PA that has no recursively saturated elementary submodel of the same cardinality as the model? I will present some partial results involving partial inductive satisfaction classes.
- - - - Wednesday, Apr 14, 2021 - - - -
- - - - Thursday, Apr 15, 2021 - - - -
Philog Seminar
Thursday, April 15, 6:30 PM
What does it mean that an event C ``actually caused'' event E?
The problem of defining actual causation goes beyond mere philosophical
speculation. For example, in many legal arguments, it is precisely what
needs to be established in order to determine responsibility. (What exactly
was the actual cause of the car accident or the medical problem?)
The philosophy literature has been struggling with the problem
of defining causality since the days of Hume, in the 1700s.
Many of the definitions have been couched in terms of counterfactuals.
(C is a cause of E if, had C not happened, then E would not have happened.)
In 2001, Judea Pearl and I introduced a new definition of actual cause,
using Pearl's notion of structural equations to model
counterfactuals. The definition has been revised twice since then,
extended to deal with notions like "responsibility" and "blame", and
applied in databases and program verification. I survey
the last 15 years of work here, including joint work
with Judea Pearl, Hana Chockler, and Chris Hitchcock. The talk will be
completely self-contained.
A Zoom link will be posted on April 14 on https://philog.arthurpaulpedersen.org/
- - - - Friday, Apr 16, 2021 - - - -
- - - - Monday, Apr 19, 2021 - - - -
Date: Monday, April 19th, 4.15-6.15 (NY time)
Title: Brouwer’s First Act of Intuitionism
Abstract: L.E.J. Brouwer famously argued that mathematics was completely separated from formal language. His explanation for why this is so leaves room for interpretation. Indeed, one might ask: what sort of philosophical background is required to make sense of the strong anti-linguistic views of Brouwer? In this talk, we outline some possible answers to the above. We then present an interpretation that we argue best makes sense of Brouwer’s first act.
- - - - Tuesday, Apr 20, 2021 - - - -
- - - - Wednesday, Apr 21, 2021 - - - -
- - - - Thursday, Apr 22, 2021 - - - -
- - - - Friday, Apr 23, 2021 - - - -
- - - - Web Site - - - -
"Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)"
-------- ADMINISTRIVIA --------
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If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Logic Seminar 14 April 2021 17:00 hrs by Karen Seidel, HPI, University of Potsdam
Barcelona Set theory Seminar
This Week in Logic at CUNY
Date: Monday, April 12th, 4.15-6.15 (NY time)
Abstract: Bolzano is famously responsible for an influential substitutional account of logical consequence (or, as he calls it, logical deducibility): a proposition, 𝜑, is logically deducible from a set of propositions, Γ, iff every uniform substitution of non-logical ideas in Γ∪{𝜑} that makes every proposition in Γ true also makes 𝜑 true. There are two problems with making sense of Bolzano’s proposal, however. One is that Bolzano argues that every proposition is of the form a has B—in other words, is a monadic atomic predication. So, for Bolzano, logically complex propositions like ‘𝜑 and 𝜓’ cannot have the semantic structure they appear to. This can be addressed, roughly, by taking complex propositions to predicate logical ideas of collections of propositions. But this introduces the second problem: for Bolzano, familiar logical ideas like ‘and’, ‘or’, and ‘not’ are complex ideas with compositional structure. I’ll show that, as a result of this structure, we cannot use the simple and familiar notion of uniform substitution in order to understand logical deducibility. We must instead use what I’ll call form-sensitive substitution. I will end by drawing some general lessons about substitutional definitions of logical consequence in languages with the resources to generate complex predicates of propositions.
- - - - Tuesday, Apr 13, 2021 - - - -
Roman Kossak, CUNY
Automorphisms, Jónsson Models, and Satisfaction Classes
25 years ago I wrote a paper on four open problems concerning recursively saturated models of PA. The problems are still open. I will talk about two of them: (1) Let M be a countable recursively saturated model of PA. Can every automorphism of M be extended to some recursively saturated elementary end extension of M? (2) Is there a recursively saturated model of PA that has no recursively saturated elementary submodel of the same cardinality as the model? I will present some partial results involving partial inductive satisfaction classes.
- - - - Wednesday, Apr 14, 2021 - - - -
- - - - Thursday, Apr 15, 2021 - - - -
Philog Seminar
Thursday, April 8, 6:30 PM
Speaker: Joseph Halpern, Cornell
- - - - Friday, Apr 16, 2021 - - - -
- - - - Monday, Apr 19, 2021 - - - -
Date: Monday, April 19th, 4.15-6.15 (NY time)
Title: Brouwer’s First Act of Intuitionism
Abstract: L.E.J. Brouwer famously argued that mathematics was completely separated from formal language. His explanation for why this is so leaves room for interpretation. Indeed, one might ask: what sort of philosophical background is required to make sense of the strong anti-linguistic views of Brouwer? In this talk, we outline some possible answers to the above. We then present an interpretation that we argue best makes sense of Brouwer’s first act.
- - - - Tuesday, Apr 20, 2021 - - - -
- - - - Wednesday, Apr 21, 2021 - - - -
- - - - Thursday, Apr 22, 2021 - - - -
- - - - Friday, Apr 23, 2021 - - - -
- - - - Web Site - - - -
"Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)"
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Unusual time for tomorrow talk by Joerg Brendle (10:30 am Toronto time)
Unusual time for Friday 9th talk by Joerg Brendle (10:30 am Toronto time)
This Week in Logic at CUNY
- - - - Monday, Apr 5, 2021 - - - -
Spring 2021
Date: Monday, April 5th, 4.15-6.15 (NY time)
Speakers: Federico Pailos and Eduardo Barrio (Buenos Aires)
Title: A Metainferential Solution to the Adoption Problem
Abstract: In ‘The Question of Logic’ (Kripke 2020) and “The Adoption Problem and the Epistemology of Logic” (Padró 2020), Kripke and Padró argue against the possibility of adopting an alternative logic. Without having already endorsed a logic, it is not possible to derive the consequences of an alternative system. In particular, without Modus Ponens in the metatheory, one could not adopt any inferential rule at all. This seems to cause trouble for logics like LP, that does not validate this rule. Modus Ponens is a self-governing rule that cannot be adopted and could not be rejected. This is connected with the problem of the tortoise reasoner (Scambler 2019) and the problem of the tortoise Logic (Priest 2021). In this talk, we offer a new solution. With the metainferential logic TS/LP it is possible to model metalogical Modus Ponens-like reasoning while still rejecting Modus Ponens.
- - - - Tuesday, Apr 6, 2021 - - - -
Topless powerset preserving end-extensions and rank-extensions of countable models of set theory
This talk will report on ongoing work that is being done in collaboration with Ali Enayat (University of Gothenburg).
For models of set theory N and M, N is a powerset preserving end-extension of M if N is an end-extension of M and N contains no new subsets of sets in M. A model of Kripke-Platek Set Theory, N, is a rank-extension of a model of Kripke-Platek Set Theory, M, if N is an end-extension of M and all of the new sets in N have rank that exceeds the rank of all of the sets in M. A powerset preserving end-extension (rank-extension) N of M is topless if M≠N and there is no set in N∖M containing only sets from M. If M=⟨M,EM⟩ is a model of set theory, then the admissible cover of M, CovM, is defined to be the smallest admissible structure with M forming its urelements and whose language contains a unary function function symbol, F, that sends each m∈M to the set {x∈M∣xEMm}. Barwise has shown that if M is a model of Kripke-Platek Set Theory, then CovM exists and its minimality facilitates compactness arguments for infinitary languages coded in CovM. We extend Barwise's analysis by showing that if M satisfies enough set theory then the expansion of CovM obtained by adding the powerset function remains admissible. This allows us to build powerset preserving end-extensions and rank-extensions of countable models of certain subsystems of ZFC satisfying any given recursive subtheory of the model being extended. In particular, we show that
- Every countable model of KPP has a topless rank-extension that satisfies KPP.
- Every countable ω-standard model of MOST+Π1-collection has a topless powerset preserving end-extension that satisfies MOST+Π1-collection.
- - - - Wednesday, Apr 7, 2021 - - - -
- - - - Thursday, Apr 8, 2021 - - - -
Philog Seminar
Thursday, April 8, 6:30 PM
Speaker: Jongjin (JJ) Kim (Korea University)
Abstract. We discuss two approaches to life: presentism and futurism. We locate presentism within various elements of Buddhism, in the form of advice to live in the present and not to allow the future to hinder us from living in the ever present now. By contrast, futurism, which we identify with Karl Popper, advises us to think of future consequences before we act, and to act now for a better future. Of course, with its emphasis on a well-defined path to an ideal future ideally culminating in enlightenment, Buddhism undoubtedly has elements of futurism as well. We do not intend to determine which of these two approaches to time is more dominant in Buddhism, nor how the two approaches are best understood within Buddhism; but simply we intend to compare and contrast these two approaches, using those presentist elements of Buddhism as representative of presentism while contrasting them with those elements of futurism to be found in Popper and others. We will discuss various aspects of presentism and futurism, such as Ruth Millikan’s Popperian animal, the psychologist Howard Rachlin’s social and temporal discounting, and even the popular but controversial idea, YOLO (you only live once). The primary purpose of this paper is to contrast one with the other. The central question of ethics is: How should one live? Our variation on that question is: When should one live? We conjecture that the notion of flow, developed by Csikszentmihalyi, may be a better optimal choice between these two positions.
Jongjin Kim received his doctorate in Philosophy from CUNY in 2019.
For Zoom link please go to https://philog.arthurpaulpedersen.org/
on Wednesday
- - - - Friday, Apr 9, 2021 - - - -
Sandra Müller, University of Vienna
The exact consistency strength of 'AD + all sets are universally Baire'
The large cardinal strength of the Axiom of Determinacy when enhanced with the hypothesis that all sets of reals are universally Baire is known to be much stronger than the Axiom of Determinacy itself. In fact, Sargsyan conjectured it to be as strong as the existence of a cardinal that is both a limit of Woodin cardinals and a limit of strong cardinals. Larson, Sargsyan and Wilson showed that this would be optimal via a generalization of Woodin’s derived model construction. We will discuss a new translation procedure for hybrid mice extending work of Steel, Zhu and Sargsyan and use this to prove Sargsyan’s conjecture.
- - - - Monday, Apr 12, 2021 - - - -
Date: Monday, April 5th, 4.15-6.15 (NY time)
Abstract: Bolzano is famously responsible for an influential substitutional account of logical consequence (or, as he calls it, logical deducibility): a proposition, 𝜑, is logically deducible from a set of propositions, Γ, iff every uniform substitution of non-logical ideas in Γ∪{𝜑} that makes every proposition in Γ true also makes 𝜑 true. There are two problems with making sense of Bolzano’s proposal, however. One is that Bolzano argues that every proposition is of the form a has B—in other words, is a monadic atomic predication. So, for Bolzano, logically complex propositions like ‘𝜑 and 𝜓’ cannot have the semantic structure they appear to. This can be addressed, roughly, by taking complex propositions to predicate logical ideas of collections of propositions. But this introduces the second problem: for Bolzano, familiar logical ideas like ‘and’, ‘or’, and ‘not’ are complex ideas with compositional structure. I’ll show that, as a result of this structure, we cannot use the simple and familiar notion of uniform substitution in order to understand logical deducibility. We must instead use what I’ll call form-sensitive substitution. I will end by drawing some general lessons about substitutional definitions of logical consequence in languages with the resources to generate complex predicates of propositions.
- - - - Tuesday, Apr 13, 2021 - - - -
Roman Kossak, CUNY
Automorphisms, Jónsson Models, and Satisfaction Classes
25 years ago I wrote a paper on four open problems concerning recursively saturated models of PA. The problems are still open. I will talk about two of them: (1) Let M be a countable recursively saturated model of PA. Can every automorphism of M be extended to some recursively saturated elementary end extension of M? (2) Is there a recursively saturated model of PA that has no recursively saturated elementary submodel of the same cardinality as the model? I will present some partial results involving partial inductive satisfaction classes.
- - - - Wednesday, Apr 14, 2021 - - - -
- - - - Thursday, Apr 15, 2021 - - - -
- - - - Friday, Apr 16, 2021 - - - -
Conference announcement: Boise Extravaganza in Set Theory (BEST) June 17-20
The 2021 Boise Extravaganza in Set Theory will take place in Zoomland during June 17-20. We would be delighted if you will attend! (Please follow https://www.boisestate.edu/math/best for future updates.)
- - - - Web Site - - - -
"Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)"
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Barcelona Set theory Seminar
Logic Seminar 7 April 2021 17:00 hrs at NUS by Frank Stephan
Logic Seminar Tomorrow in Singapore
Logic Seminar Wednesday 31 March 2021
This Week in Logic at CUNY
- - - - Monday, Mar 29, 2021 - - - -
- - - - Tuesday, Mar 30, 2021 - - - -
Residue rings of models of Peano Arithmetic
- - - - Wednesday, Mar 31, 2021 - - - -
- - - - Thursday, Apr 1, 2021 - - - -
- - - - Friday, Apr 2, 2021 - - - -
The approximation property and generic embeddings
The approximation property was introduced by Hamkins for his Gap Forcing Theorem, and it has turned out to be a very useful notion, appearing for example in the partial equiconsistency result of Viale and Weiss on PFA, and in the proof of Woodin's HOD Dichotomy Theorem. In the context of generic embeddings, there can be a useful interplay between elementarity and approximation. We discuss some recent work in this direction: (1) tensions between saturated ideals on ω2 and the tree property (with Sean Cox), (2) fragility of the strong independence spectra (with Vera Fischer), and (3) mutual inconsistency of Foreman‘s minimal generic hugeness axioms.
- - - - Monday, Apr 5, 2021 - - - -
- - - - Tuesday, Apr 6, 2021 - - - -
TBA
- - - - Wednesday, Apr 7, 2021 - - - -
- - - - Thursday, Apr 8, 2021 - - - -
- - - - Friday, Apr 9, 2021 - - - -
Conference announcement: Boise Extravaganza in Set Theory (BEST) June 17-20
The 2021 Boise Extravaganza in Set Theory will take place in Zoomland during June 17-20. We would be delighted if you will attend! (Please follow https://www.boisestate.edu/math/best for future updates.)
- - - - Web Site - - - -
"Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)"
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Unusual time for tomorrow talk by Sakaé Fuchino (10:30 am Toronto time)
$\utpoQ$\vspace{-0.5\smallskipamount} \st\ $\forces{\poP}{\utpoQ\in\calP}$, we have
$\poP\ast\utpoQ\in\calP$.
For an iterable class $\mathcal{P}$ of posets, a cardinal $\mu$ is called {\it Laver-generically
supercompact for $\mathcal{P}$}, if, for any $\mathbb{P}\in\mathcal{P}$ and $\lambda\in\On$,
there is a $\poP$-name $\utpoQ$\vspace{-0.5\smallskipamount} with $\forces{\poP}{\utpoQ\in\calP}$ \st, letting
$\poQ=\poP\ast\utpoQ$,
there are $j$, $M\subseteq\uniV[\genH]$ for $(\uniV, \mathbb{Q})$-generic
$\genH$ such that
1) $\elembed{j}{V}{M}$,\smallskip
2) $crit(j)=\mu$, $j(\mu)>\lambda$,\smallskip
3) $\cardof{\poQ}\leq j(\mu)$,\smallskip
4) $\poP$, $\genH\in M$ and \smallskip
5) $j\imageof\lambda\in M$.\\\\
The notion of Laver-generically superhugeness is obtained when \assert{5} is replaced by
The notion of Laver-generically large cardinal for $\calP$ given here is stronger than the one
introduced in \cite{II} and is called there the {\it strongly} and {\it tightly}
Laver-generically large cardinal (the strongness corresponds the usage of two-step
iteration in the definition instead of just $\poP\circleq\poQ$, and the tightness the
condition \assert{3}).
In my talk, I will give a proof of the following:\quad
For many natural iterable class of proper posets $\mathcal{P}$, a
Laver-generically supercompact cardinal $\mu$ for $\poP$ is either $\aleph_2$ or very large (if it
exists),
and the continuum is either $\aleph_1$ or $\aleph_2$, or $\geq\mu$ in case of very large
$\mu$, where it depends on $P$ which scenario we have.
If time allows, I will also sketch a proof of the following theorem:\quad
If $\mathcal{P}$ is the class of c.c.c.\ posets (or some other iterable class $\calP$ of posets preserving all
cardinalities but adding some real), and if $\mu$ is Laver-generically superhuge for $\mathcal{P}$, then
$\mu=2^{\aleph_0}$.
At the moment, it is open if the same theorem holds for a Laver-generically supercompact
(KGRC) research seminar talk on Thursday, March 25
This Week in Logic at CUNY
- - - - Monday, Mar 15, 2021 - - - -
Logic and Metaphysics Workshop
Date: Monday, Mar 15, 4.15-6.15 (NY time)
Title: Belief Content and Rationality: Why Racist Beliefs Are Not Rational
Abstract: I present a novel defense of the evidentialist thesis in the debate between epistemologists who defend this thesis and those who defend the moral encroachment thesis. Both sides of the moral encroachment-evidentialism debate suppose that the belief class of what I call seemingly-rational-racist beliefs obtains. I reject that this belief class of seemingly- rational-racist beliefs obtains on the basis that beliefs with this kind of content are false and evidentially unsupported. I submit that they are false and evidentially unsupported because of how the content of these beliefs relate to the social-linguistic practices and habits that compose racial injustice in the US and other similarly colonized societies. I diagnose that a problem with this debate is that both sides in this debate conceive of the content of race terms and beliefs that attribute negative features to Black, Indigenous and Latinx persons without considering how they function in a racially unjust society.
- - - - Tuesday, Mar 16, 2021 - - - -
- - - - Wednesday, Mar 17, 2021 - - - -
Speaker: Tobias Fritz, University of Innsbruck.
Date and Time: Wednesday March 17, 2021, 7:00 - 8:30 PM., on Zoom.
Title: Categorical Probability and the de Finetti Theorem.
Abstract: I will give an introduction to categorical probability in terms of Markov categories, followed by a discussion of the classical de Finetti theorem within that framework. Depending on whether current ideas work out or not, I may (or may not) also present a sketch of a purely categorical proof of the de Finetti theorem based on the law of large numbers. Joint work with Tomáš Gonda, Paolo Perrone and Eigil Fjeldgren Rischel.
- - - - Thursday, Mar 18, 2021 - - - -
- - - - Friday, Mar 19, 2021 - - - -
Paul Blain Levy, University of Birmingham
Broad Infinity and Generation Principles
Broad Infinity is a new and arguably intuitive axiom scheme in set theory. It states that 'broad numbers', which are three-dimensional trees whose growth is controlled, form a set. If the Axiom of Choice is assumed, then Broad Infinity is equivalent to the Ord-is-Mahlo scheme: every closed unbounded class of ordinals contains a regular ordinal.
Whereas the axiom of Infinity leads to generation principles for sets and families and ordinals, Broad Infinity leads to more advanced versions of these principles. The talk explains these principles and how they are related under various prior assumptions: the Axiom of Choice, the Law of Excluded Middle, and weaker assumptions.
Next Week in Logic at CUNY:
- - - - Monday, Mar 22, 2021 - - - -
Logic and Metaphysics Workshop
Date: Monday, Mar 1, 4.15-6.15 (NY time)
Martin Pleitz (Münster).
Title: Dualism about Generality
Abstract: In my talk I will motivate, outline, and apply a variant of first order predicate logic that can distinguish between two kinds of generality, which I call objectual generality and conceptual generality. To see the difference, compare the two general statements ‘Every human is a featherless biped’ and ‘Every human is a rational animal’. On a charitable understanding, the first sentence is about all humans past and present, as a subcollection of all particular objects currently accessible to us, while the second sentence is not about any particular object at all, but about the interaction of the concepts of being human and being a rational animal. Historically, the quantified sentences of predicate logic have been understood in either of the two ways. Frege understood them as expressing conceptual generalities; hence it was natural for him to call his predicate logic a “Concept Script”. Today, they are usually understood as objectual generalities, manifest both in the idea that a quantified sentence is like a conjunction (or disjunction) of its instances and in the current model theoretic orientation in semantics. But as we can find ourselves in a situation where we want to talk about both kinds of generality (and their interaction), it is worthwhile to develop the resources to express them within a single system. I will outline such a system that results from adding a second pair of quantifiers to regular first order predicate logic, and sketch applications to the notion of analyticity, natural kind predicates, and an ontological argument.
- - - - Tuesday, Mar 23, 2021 - - - -
Mateusz Łełyk, University of Warsaw
Nonequivalent axiomatizations of PA and the Tarski Boundary: Part III
This is a continuation of the talk from Feb 16th. This time we shall study different theories of the form CT−[δ] which are conservative extensions of a PA. In particular, we prove the following theorem.
Theorem 2 There exists a family {δf}f∈ω∗ such that for all f,g∈ω∗
1) CT−[δf] is conservative over PA;
2) if f⊊g, then CT−[δg] properly extends CT−[δf];
3) if f⊥g then CT−[δg]∪CT−[δf] is nonconservative over PA (but consistent).
We will finish the proof of the theorem announced in the abstract of part II.
- - - - Wednesday, Mar 24, 2021 - - - -
- - - - Thursday, Mar 25, 2021 - - - -
Philog Seminar
6:30 PM, Thursday, March 25
Rohit Parikh (CUNY) on
The Logic of Knowledge Based Obligation (joint work with Eric Pacuit (UMD) and Eva Cogan (Brooklyn))
Our obligations depend on what we know. If we do not know that we need to do X then there is no obligation to actually do X. However, sometimes there is also an obligation to know and hence also an obligation to inform. We look into the temporal logic of such issues, relying on work by John Horty and by Parikh and Ramanujam.
- - - - Friday, Mar 26, 2021 - - - -
The 'algebraic' vs. 'non-algebraic' distinction: New impulses for the universe/multiverse debate?
The distinction between 'algebraic' and 'non-algebraic fields in mathematics, coined by Shapiro (1997), plays an important role in discussions about the status of set theory and connects back to the so-called universe/multiverse debate in the philosophy of set theory. In this talk we will see, that this distinction is not as clear cut as is usually assume when using it in the debate. In particular, we will see that in more recent formulations of this distinction, multiversism seems to split into a a strong and a weaker form. This can be translated to a meta-level, when considering the background theory in which set-theoretic multiversism can take place. This offers a more fine-grained picture of multiversism and allows us to mitigate a standard universist objection based on the conception of a multiversist background theory.
- - - - Monday, Mar 29, 2021 - - - -
- - - - Tuesday, Mar 30, 2021 - - - -
TBA
- - - - Wednesday, Mar 31, 2021 - - - -
- - - - Thursday, Apr 1, 2021 - - - -
- - - - Friday, Apr 2, 2021 - - - -
TBA
Conference announcement: Boise Extravaganza in Set Theory (BEST) June 17-20
The 2021 Boise Extravaganza in Set Theory will take place in Zoomland during June 17-20. We would be delighted if you will attend! (Please follow https://www.boisestate.edu/math/best for future updates.)
- - - - Web Site - - - -
"Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)"
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
UPDATE: This Week in Logic at CUNY
- - - - Monday, Mar 22, 2021 - - - -
Logic and Metaphysics Workshop
Date: Monday, Mar 1, 4.15-6.15 (NY time)
Martin Pleitz (Münster).
Title: Dualism about Generality
Abstract: In my talk I will motivate, outline, and apply a variant of first order predicate logic that can distinguish between two kinds of generality, which I call objectual generality and conceptual generality. To see the difference, compare the two general statements ‘Every human is a featherless biped’ and ‘Every human is a rational animal’. On a charitable understanding, the first sentence is about all humans past and present, as a subcollection of all particular objects currently accessible to us, while the second sentence is not about any particular object at all, but about the interaction of the concepts of being human and being a rational animal. Historically, the quantified sentences of predicate logic have been understood in either of the two ways. Frege understood them as expressing conceptual generalities; hence it was natural for him to call his predicate logic a “Concept Script”. Today, they are usually understood as objectual generalities, manifest both in the idea that a quantified sentence is like a conjunction (or disjunction) of its instances and in the current model theoretic orientation in semantics. But as we can find ourselves in a situation where we want to talk about both kinds of generality (and their interaction), it is worthwhile to develop the resources to express them within a single system. I will outline such a system that results from adding a second pair of quantifiers to regular first order predicate logic, and sketch applications to the notion of analyticity, natural kind predicates, and an ontological argument.
- - - - Tuesday, Mar 23, 2021 - - - -
Mateusz Łełyk, University of Warsaw
Nonequivalent axiomatizations of PA and the Tarski Boundary: Part III
This is a continuation of the talk from Feb 16th. This time we shall study different theories of the form CT−[δ] which are conservative extensions of a PA. In particular, we prove the following theorem.
Theorem 2 There exists a family {δf}f∈ω∗ such that for all f,g∈ω∗
1) CT−[δf] is conservative over PA;
2) if f⊊g, then CT−[δg] properly extends CT−[δf];
3) if f⊥g then CT−[δg]∪CT−[δf] is nonconservative over PA (but consistent).
We will finish the proof of the theorem announced in the abstract of part II.
- - - - Wednesday, Mar 24, 2021 - - - -
- - - - Thursday, Mar 25, 2021 - - - -
Philog Seminar
6:30 PM, Thursday, March 25
Rohit Parikh (CUNY) on
The Logic of Knowledge Based Obligation (joint work with Eric Pacuit (UMD) and Eva Cogan (Brooklyn))
Our obligations depend on what we know. If we do not know that we need to do X then there is no obligation to actually do X. However, sometimes there is also an obligation to know and hence also an obligation to inform. We look into the temporal logic of such issues, relying on work by John Horty and by Parikh and Ramanujam.
- - - - Friday, Mar 26, 2021 - - - -
The 'algebraic' vs. 'non-algebraic' distinction: New impulses for the universe/multiverse debate?
The distinction between 'algebraic' and 'non-algebraic fields in mathematics, coined by Shapiro (1997), plays an important role in discussions about the status of set theory and connects back to the so-called universe/multiverse debate in the philosophy of set theory. In this talk we will see, that this distinction is not as clear cut as is usually assume when using it in the debate. In particular, we will see that in more recent formulations of this distinction, multiversism seems to split into a a strong and a weaker form. This can be translated to a meta-level, when considering the background theory in which set-theoretic multiversism can take place. This offers a more fine-grained picture of multiversism and allows us to mitigate a standard universist objection based on the conception of a multiversist background theory.
- - - - Monday, Mar 29, 2021 - - - -
- - - - Tuesday, Mar 30, 2021 - - - -
TBA
- - - - Wednesday, Mar 31, 2021 - - - -
- - - - Thursday, Apr 1, 2021 - - - -
- - - - Friday, Apr 2, 2021 - - - -
TBA
Conference announcement: Boise Extravaganza in Set Theory (BEST) June 17-20
The 2021 Boise Extravaganza in Set Theory will take place in Zoomland during June 17-20. We would be delighted if you will attend! (Please follow https://www.boisestate.edu/math/best for future updates.)
- - - - Web Site - - - -
"Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)"
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Barcelona Set theory Seminar
Unusual time for Friday 26th talk by Sakae Fuchino (10:30 am)
$\utpoQ$\vspace{-0.5\smallskipamount} \st\ $\forces{\poP}{\utpoQ\in\calP}$, we have
$\poP\ast\utpoQ\in\calP$.
For an iterable class $\mathcal{P}$ of posets, a cardinal $\mu$ is called {\it Laver-generically
supercompact for $\mathcal{P}$}, if, for any $\mathbb{P}\in\mathcal{P}$ and $\lambda\in\On$,
there is a $\poP$-name $\utpoQ$\vspace{-0.5\smallskipamount} with $\forces{\poP}{\utpoQ\in\calP}$ \st, letting
$\poQ=\poP\ast\utpoQ$,
there are $j$, $M\subseteq\uniV[\genH]$ for $(\uniV, \mathbb{Q})$-generic
$\genH$ such that
1) $\elembed{j}{V}{M}$,\smallskip
2) $crit(j)=\mu$, $j(\mu)>\lambda$,\smallskip
3) $\cardof{\poQ}\leq j(\mu)$,\smallskip
4) $\poP$, $\genH\in M$ and \smallskip
5) $j\imageof\lambda\in M$.\\\\
The notion of Laver-generically superhugeness is obtained when \assert{5} is replaced by
The notion of Laver-generically large cardinal for $\calP$ given here is stronger than the one
introduced in \cite{II} and is called there the {\it strongly} and {\it tightly}
Laver-generically large cardinal (the strongness corresponds the usage of two-step
iteration in the definition instead of just $\poP\circleq\poQ$, and the tightness the
condition \assert{3}).
In my talk, I will give a proof of the following:\quad
For many natural iterable class of proper posets $\mathcal{P}$, a
Laver-generically supercompact cardinal $\mu$ for $\poP$ is either $\aleph_2$ or very large (if it
exists),
and the continuum is either $\aleph_1$ or $\aleph_2$, or $\geq\mu$ in case of very large
$\mu$, where it depends on $P$ which scenario we have.
If time allows, I will also sketch a proof of the following theorem:\quad
If $\mathcal{P}$ is the class of c.c.c.\ posets (or some other iterable class $\calP$ of posets preserving all
cardinalities but adding some real), and if $\mu$ is Laver-generically superhuge for $\mathcal{P}$, then
$\mu=2^{\aleph_0}$.
At the moment, it is open if the same theorem holds for a Laver-generically supercompact
Talk tomorrow by Anush Tserunyan (1 30 pm in new daylight saving time)
Two CMU seminars on Tuesday, March 23
Reminder of talk today at 10:00 hrs
Logic Seminar 24 March 2021 17:00 hrs at NUS by Philipp Schlicht
(KGRC) research seminar talk on Thursday, March 18
Barcelona Set theory Seminar
This Friday talk by Anush Tserunyan (1 30 pm in new daylight saving time)
This Week in Logic at CUNY
- - - - Monday, Mar 15, 2021 - - - -
Logic and Metaphysics Workshop
Date: Monday, Mar 15, 4.15-6.15 (NY time)
Title: Belief Content and Rationality: Why Racist Beliefs Are Not Rational
Abstract: I present a novel defense of the evidentialist thesis in the debate between epistemologists who defend this thesis and those who defend the moral encroachment thesis. Both sides of the moral encroachment-evidentialism debate suppose that the belief class of what I call seemingly-rational-racist beliefs obtains. I reject that this belief class of seemingly- rational-racist beliefs obtains on the basis that beliefs with this kind of content are false and evidentially unsupported. I submit that they are false and evidentially unsupported because of how the content of these beliefs relate to the social-linguistic practices and habits that compose racial injustice in the US and other similarly colonized societies. I diagnose that a problem with this debate is that both sides in this debate conceive of the content of race terms and beliefs that attribute negative features to Black, Indigenous and Latinx persons without considering how they function in a racially unjust society.
- - - - Tuesday, Mar 16, 2021 - - - -
- - - - Wednesday, Mar 17, 2021 - - - -
Speaker: Tobias Fritz, University of Innsbruck.
Date and Time: Wednesday March 17, 2021, 7:00 - 8:30 PM., on Zoom.
Title: Categorical Probability and the de Finetti Theorem.
Abstract: I will give an introduction to categorical probability in terms of Markov categories, followed by a discussion of the classical de Finetti theorem within that framework. Depending on whether current ideas work out or not, I may (or may not) also present a sketch of a purely categorical proof of the de Finetti theorem based on the law of large numbers. Joint work with Tomáš Gonda, Paolo Perrone and Eigil Fjeldgren Rischel.
- - - - Thursday, Mar 18, 2021 - - - -
- - - - Friday, Mar 19, 2021 - - - -
Paul Blain Levy, University of Birmingham
Broad Infinity and Generation Principles
Broad Infinity is a new and arguably intuitive axiom scheme in set theory. It states that 'broad numbers', which are three-dimensional trees whose growth is controlled, form a set. If the Axiom of Choice is assumed, then Broad Infinity is equivalent to the Ord-is-Mahlo scheme: every closed unbounded class of ordinals contains a regular ordinal.
Whereas the axiom of Infinity leads to generation principles for sets and families and ordinals, Broad Infinity leads to more advanced versions of these principles. The talk explains these principles and how they are related under various prior assumptions: the Axiom of Choice, the Law of Excluded Middle, and weaker assumptions.
Next Week in Logic at CUNY:
- - - - Monday, Mar 22, 2021 - - - -
Logic and Metaphysics Workshop
Date: Monday, Mar 1, 4.15-6.15 (NY time)
Martin Pleitz (Münster).
Title: Dualism about Generality
Abstract: In my talk I will motivate, outline, and apply a variant of first order predicate logic that can distinguish between two kinds of generality, which I call objectual generality and conceptual generality. To see the difference, compare the two general statements ‘Every human is a featherless biped’ and ‘Every human is a rational animal’. On a charitable understanding, the first sentence is about all humans past and present, as a subcollection of all particular objects currently accessible to us, while the second sentence is not about any particular object at all, but about the interaction of the concepts of being human and being a rational animal. Historically, the quantified sentences of predicate logic have been understood in either of the two ways. Frege understood them as expressing conceptual generalities; hence it was natural for him to call his predicate logic a “Concept Script”. Today, they are usually understood as objectual generalities, manifest both in the idea that a quantified sentence is like a conjunction (or disjunction) of its instances and in the current model theoretic orientation in semantics. But as we can find ourselves in a situation where we want to talk about both kinds of generality (and their interaction), it is worthwhile to develop the resources to express them within a single system. I will outline such a system that results from adding a second pair of quantifiers to regular first order predicate logic, and sketch applications to the notion of analyticity, natural kind predicates, and an ontological argument.
- - - - Tuesday, Mar 23, 2021 - - - -
- - - - Wednesday, Mar 24, 2021 - - - -
- - - - Thursday, Mar 25, 2021 - - - -
- - - - Friday, Mar 26, 2021 - - - -
- - - - Web Site - - - -
"Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)"
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Talk tomorrow by Anush Tserunyan (1 30 pm)
Talk by Anush Tserunyan Friday 19th (1 30 pm)
CMU seminars on Tuesday, March 16
Tomorrow talk by Menachem Kojman (1 30 pm)
Boise Extravaganza in Set Theory June 17-20
Logic Seminar 18 March 2021 10:00 hrs at NUS by Ko Liling (Notre Dame)
Peter Koellner: Minimal Models and β-Categoricity
(KGRC) research seminar talk on Thursday, March 11
Logic Seminar 10 March 2021 17:00 hrs at NUS
Talk by Menachem Kojman this Friday 12th (1 30 pm)
Barcelona Set theory Seminar
Upcoming CMU mathematical logic seminars
Talk tomorrow by Alan Dow (1 30 pm)
Alexandra Pasi: Forcing $\aleph_1$-Free Groups to Be Free
Fwd: Fw: Kobe Set Theory Workshop 2021 -- on the occasion of Sakaé Fuchino's retirement --
Sent: Tuesday, March 2, 2021 4:58 AM
To: brendle <brendle@kobe-u.ac.jp>; SAKAI Hiroshi <hsakai@people.kobe-u.ac.jp>
Subject: Kobe Set Theory Workshop 2021 -- on the occasion of Sakaé Fuchino's retirement --
Talk this Friday by Alan Dow (1 30 pm)
Kobe Set Theory Workshop 2021: March 9-11
(KGRC) research seminar talk on Thursday, March 4
This Week in Logic at CUNY
Date: Monday, Mar 1, 4.15-6.15 (NY time)
Title: The Easy Argument Against Noncontractive Logics Doesn’t Work
Abstract: The Easy Argument against noncontractivism is the argument that essentially amounts to pointing out that contraction is just repeating oneself. The purpose of this talk is to explain why the Easy Argument fails. I show first that the Easy Argument fails by being insufficiently precise, since there are many ways we can combine premises in an argument. After correcting for this, the Easy Argument then fails by being straightforwardly invalid. The premises required to correct for *this* failure, however, have controversial consequences. Altogether, it seems arguments against noncontractive logics, if there are any, will be Hard—not Easy—Arguments.
- - - - Tuesday, Mar 2, 2021 - - - -
Ali Enayat, University of Gothenburg
PA with a class of indiscernibles
This talk focuses on the theory PAI (I for Indiscernibles), a theory formulated in the language of PA augmented with a unary predicate I(x). Models of PAI are of the form (M,I) where (1) M is a model of PA, (2) I is a proper class of M, i.e., I is unbounded in M and (M,I) satisfies PA*, and (3) I forms a class of indiscernibles over M. The formalizability of the Infinite Ramsey Theorem in PA makes it clear that PAI is a conservative extension of PA. As we will see, nonstandard models of PA (of any cardinality) that have an expansion to a model of PAI are precisely those nonstandard models PA that can carry an inductive partial satisfaction class. The formulation and investigation of PAI was inspired by my work on the set theoretical sibling ZFI of PAI, whose behavior I will also compare and contrast with that of PAI.
- - - - Wednesday, Mar 3, 2021 - - - -
Speaker: Joshua Sussan, Medgar Evers, CUNY.
Title: Categorification and quantum topology.
Abstract: The Jones polynomial of a link could be defined through the representation theory of quantum sl(2). It leads to a 3-manifold invariant and 2+1 dimensional TQFT. In the mid 1990s, Crane and Frenkel outlined the categorification program with the aim of constructing a 3+1 dimensional TQFT by upgrading the representation theory of quantum sl(2) to some categorical structures. We will review these ideas and give examples of various categorifications of quantum sl(2) constructions.
- - - - Thursday, Mar 4, 2021 - - - -
Philog seminar
Thursday March 4 at 6:30 PM
Jenn McDonald, CUNY Graduate Center
Causal Models as Relative to Modal Profile
Abstract A recent development in the philosophy of causation uses the framework of causal models, such as structural equation models, to define actual causation. There are two components to such a definition. The first is to identify how to define causation in terms of a given model or given class of models. The second is to provide an account of what qualifies models as given – or apt – such that they can be plugged into the first stage. A naïve hypothesis is that a model is apt just in case it is accurate. In this talk I will argue, however, that the accuracy of a model is not a determinate function of a model, an interpretation, and a situation. A given model on a given interpretation can still be deemed accurate or inaccurate of the same situation. As I demonstrate, this is because accuracy is relative to a set of background possibilities – what I call a modal profile. I argue that this reveals a heretofore hidden element in how causal models represent – that models represent situations only relative to some modal profile or other. I propose that this calls for an additional component of an interpretation: an interpretation is an assignment of content to the variables and a specification of modal profile.
A zoom link will be posted on https://philog.arthurpaulpedersen.org/
Next speaker: Nur Dean, Farmingdale College
- - - - Friday, Mar 5, 2021 - - - -
Hiroshi Sakai, Kobe University
Generalized stationary reflection and cardinal arithmetic
The stationary reflection principle, which is often called the Weak Reflection Principle, is known to have many interesting consequences. As for cardinal arithmetic, it implies that λω=λ for all regular cardinal λ≥ω2. In this talk, we will discuss higher analogues of this stationary reflection principle and their consequences on cardinal arithmetic.
- - - - Monday, Mar 8, 2021 - - - -
Logic and Metaphysics Workshop
Date: Monday, Mar 8, 4.15-6.15 (NY time)
Title: Two applications of Herzberger’s semantics
Abstract: In his paper “Dimensions of truth”, Hans Herzberger develops a semantic framework that captures both classical logic and weak Kleene logic through one and the same interpretation. The aim of this talk is to apply the simple idea of Herzberger to two kinds of many-valued semantics. This application will be led by the following two questions.
(i) Is de Finetti conditional a conditional?
(ii) What do CL, K3 and LP disagree about?
Note: This is a joint work with Jonas R. B. Arenhart (Santa Catarina).
- - - - Tuesday, Mar 9, 2021 - - - -
- - - - Wednesday, Mar 10, 2021 - - - -
- - - - Thursday, Mar 11, 2021 - - - -
- - - - Friday, Mar 12, 2021 - - - -
Hossein Lamei Ramandi, Cornell University
Galvin's question on non-σ-well ordered linear orders
Assume C is the class of all linear orders L such that L is not a countable union of well ordered sets, and every uncountable subset of L contains a copy of ω1. We show it is consistent that C has minimal elements. This answers an old question due to Galvin.
- - - - Web Site - - - -
"Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)"
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Talk by Justin Moore tomorrow (1 30pm)
Logic Seminar Wed 3 March 2021 17:00 hrs at NUS
Talk by Justin Moore this Friday (1 30 pm)
Talk by Justin Moore this Friday (1 30 pm)
Talk by Justin Moore tomorrow (1 30pm)
Barcelona Set theory Seminar
Barcelona Set theory Seminar
This Week in Logic at CUNY
Date: Monday, Feb 22, 4.15-6.15 (NY time)
Title: Substructural Solutions to the Semantic Paradoxes: a Dialetheic Perspective
Abstract: Over the last decade or so, a number of writers have argued for solutions to the paradoxes of semantic self-reference which proceed by dropping some of the structural rules of inference, most notably Cut and/or Contraction. In this paper, we will examine such accounts, with a particular eye on their relationship to more familiar dialetheic accounts.
- - - - Tuesday, Feb 23, 2021 - - - -
Independence in PA: The Method of (L,n)-Models
The purpose of this talk is to exposit a method for proving independence over PA of 'mathematical' statements (whatever that means). The method uses the concept of an (L,n)-model: a finite sequence of finite L-structures for some first order L extending the language of arithmetic. The idea is that this finite sequence is intended to represent increasing approximations of a potentially infinite structure and the machinery developed allows one to translate (meta-mathematical) compactness type statements, which are easily seen to be independent of PA, into statements about finite combinatorics, which have 'mathematical content'. (L,n)-models were introduced by Shelah in the 70's in his alternative proof of the Paris-Harrington Theorem and also appears (implicitly) in his example of a true, unprovable Π01 statement of some 'mathematical' content. A similar idea was discovered independently by Kripke (unpublished). In this talk we will flesh out the details of this method and extend the general theory. This will allow us to present, in a fairly systematic fashion, proofs of the Paris-Harrington Theorem and the independence over PA of several, similar, Ramsey Theoretic statements including some which are Π01.
- - - - Wednesday, Feb 24, 2021 - - - -
- - - - Thursday, Feb 25, 2021 - - - -
Philog Seminar
Thursday, Feb 25, 6:30 PM
Rohit Parikh
Covid-19 and knowledge based computation
Abstract: the purpose of this project is to combine insights from the logic of knowledge (act according to what you know), and graph theory (spread of infection follows the edges of a graph). We show how knowledge based algorithms can be used to combine safety with economic and social activity.
A Zoom link will be posted on https://philog.arthurpaulpedersen.org/
- - - - Friday, Feb 26, 2021 - - - -
Farmer Schlutzenberg, University of Münster
(Non)uniqueness and (un)definability of embeddings beyond choice
Work in ZF and let j:Vα→Vα be an elementary, or partially elementary, embedding. One can examine the degree of uniqueness, definability or constructibility of j. For example, is there β<α such that j is the unique (partially) elementary extension of j↾Vβ? Is j definable from parameters over Vα? We will discuss some results along these lines, illustrating that answers can depend heavily on circumstances. Some of the work is due independently and earlier to Gabriel Goldberg.
- - - - Monday, Mar 1, 2021 - - - -
Date: Monday, Mar 1, 4.15-6.15 (NY time)
Title: The Easy Argument Against Noncontractive Logics Doesn’t Work
Abstract: The Easy Argument against noncontractivism is the argument that essentially amounts to pointing out that contraction is just repeating oneself. The purpose of this talk is to explain why the Easy Argument fails. I show first that the Easy Argument fails by being insufficiently precise, since there are many ways we can combine premises in an argument. After correcting for this, the Easy Argument then fails by being straightforwardly invalid. The premises required to correct for *this* failure, however, have controversial consequences. Altogether, it seems arguments against noncontractive logics, if there are any, will be Hard—not Easy—Arguments.
- - - - Tuesday, Mar 2, 2021 - - - -
Ali Enayat, University of Gothenburg
PA with a class of indiscernibles
This talk focuses on the theory PAI (I for Indiscernibles), a theory formulated in the language of PA augmented with a unary predicate I(x). Models of PAI are of the form (M,I) where (1) M is a model of PA, (2) I is a proper class of M, i.e., I is unbounded in M and (M,I) satisfies PA*, and (3) I forms a class of indiscernibles over M. The formalizability of the Infinite Ramsey Theorem in PA makes it clear that PAI is a conservative extension of PA. As we will see, nonstandard models of PA (of any cardinality) that have an expansion to a model of PAI are precisely those nonstandard models PA that can carry an inductive partial satisfaction class. The formulation and investigation of PAI was inspired by my work on the set theoretical sibling ZFI of PAI, whose behavior I will also compare and contrast with that of PAI.
- - - - Wednesday, Mar 3, 2021 - - - -
Speaker: Joshua Sussan, Medgar Evers, CUNY.
Title: Categorification and quantum topology.
Abstract: The Jones polynomial of a link could be defined through the representation theory of quantum sl(2). It leads to a 3-manifold invariant and 2+1 dimensional TQFT. In the mid 1990s, Crane and Frenkel outlined the categorification program with the aim of constructing a 3+1 dimensional TQFT by upgrading the representation theory of quantum sl(2) to some categorical structures. We will review these ideas and give examples of various categorifications of quantum sl(2) constructions.
- - - - Thursday, Mar 4, 2021 - - - -
- - - - Friday, Mar 5, 2021 - - - -
Hiroshi Sakai, Kobe University
Generalized stationary reflection and cardinal arithmetic
The stationary reflection principle, which is often called the Weak Reflection Principle, is known to have many interesting consequences. As for cardinal arithmetic, it implies that λω=λ for all regular cardinal λ≥ω2. In this talk, we will discuss higher analogues of this stationary reflection principle and their consequences on cardinal arithmetic.
- - - - Web Site - - - -
"Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)"
-------- ADMINISTRIVIA --------
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Talk by Assaf Rinot tomorrow (1 30 pm)
the others.
Abstract: Strong colorings are everywhere - they can be obtained from
analysis of basis problems, transfinite diagonalizations, oscillations,
or walks on ordinals. They give rise to interesting topological spaces
and partial orders.
In this talk, I'll be looking at all aspects mentioned above, reporting
on findings from my joint projects with Kojman, Lambie-Hanson, Inamdar,
Steprans and Zhang.
Barcelona Set theory Seminar
Talk by Assaf Rinot Friday (1 30pm)
the others.
Abstract: Strong colorings are everywhere - they can be obtained from
analysis of basis problems, transfinite diagonalizations, oscillations,
or walks on ordinals. They give rise to interesting topological spaces
and partial orders.
In this talk, I'll be looking at all aspects mentioned above, reporting
on findings from my joint projects with Kojman, Lambie-Hanson, Inamdar,
Steprans and Zhang.
This Week in Logic at CUNY
- - - - Tuesday, Feb 16, 2021 - - - -
Mateusz Łełyk, University of Warsaw
Nonequivalent axiomatizations of PA and the Tarski Boundary
We study a family of axioms expressing‘All axioms of PA are true.' (*)where PA denotes Peano Arithmetic. More precisely, each such axiom states that all axioms from a chosen axiomatization of PA are true. We start with a very natural theory of truth CT−(PA) which is a finite extension of PA in the language of arithmetic augmented with a fresh predicate T to serve as a truth predicate for the language of arithmetic. Additional axioms of this theory are straightforward translations of inductive Tarski truth conditions. To study various possible ways of expressing (*), we investigate extensions of CT−(PA) with axioms of the form∀x(δ(x)→T(x)).In the above (and throughout the whole abstract) δ(x) is an elementary formula which is proof-theoretically equivalent to the standard axiomatization of PA with the induction scheme, i.e. the equivalence∀x(Provδ(x)≡ProvPA(x)).is provable in IΣ1. For every such δ, the extension of CT−(PA) with the above axiom will be denoted CT−[δ].
In particular we shall focus on the arithmetical strength of theories CT−[δ]. The 'line' demarcating extensions of CT−(PA) which are conservative over PA from the nonconservative ones is known in the literature as the Tarski Boundary. For some time, there seemed to be the least (in terms of deductive strength) *natural* extension of CT−(PA) on the nonconservative side of the boundary, whose one axiomatization is given by CT−(PA) and Δ0 induction for the extended language (the theory is called CT0). This theory can equivalently be axiomatized by adding to CT−(PA) the natural formal representation of the statement 'All theorems of PA are true.'. We show that the situation between the Tarski Boundary and CT0 is much more interesting:
Theorem 1: For every r.e. theory Th in the language of arithmetic the following are equivalent:
1) CT0⊢ Th
2) there exists δ such that CT−[δ] and Th have the same arithmetical consequences.
Theorem 1 can be seen as a representation theorem for r.e. theories below REFω(PA) (all finite iterations of uniform reflection over PA, which is the set of arithmetical consequences of CT0): each such theory can be finitely axiomatized by a theory of the form CT−[δ], where δ is proof-theoretically reducible to PA.
Secondly, we use theories CT−[δ] to investigate the situation below the Tarski Boundary. We shall prove the following result
Theorem 2: There exists a family {δf}f∈ω<ω such that for all f,g∈ω<ω
1) CT−[δf] is conservative over PA;
2) if f⊊g, then CT−[δg] properly extends CT−[δf];
3) if f⊥g then CT−[δg]∪CT−[δf] is nonconservative over PA (but consistent).
- - - - Wednesday, Feb 17, 2021 - - - -
Title: Finiteness Spaces, Generalized Polynomial Rings and Topological Groupoids.
Abstract: The category of finiteness spaces was introduced by Thomas Ehrhard as a model of classical linear logic, where a set is equipped with a class of subsets to be thought of as finitary. Morphisms are relations preserving the finitary structure. The notion of finitary subset allows for a sharp analysis of computational structure.
Working with finiteness spaces forces the number of summands in certain calculations to be finite and thus avoid convergence questions. An excellent example of this is how Ribenboim’s theory of generalized power series rings can be naturally interpreted by assigning finiteness monoid structure to his partially ordered monoids. After Ehrhard’s linearization construction is applied, the resulting structures are the rings of Ribenboim’s construction.
There are several possible choices of morphism between finiteness spaces. If one takes structure-preserving partial functions, the resulting category is complete, cocomplete and symmetric monoidal closed. Using partial functions, we are able to model topological groupoids, when we consider composition as a partial function. We can associate to any hemicompact etale Hausdorff groupoid a complete convolution ring. This is in particular the case for the infinite paths groupoid associated to any countable row-finite directed graph.
- - - - Thursday, Feb 18, 2021 - - - -
- - - - Friday, Feb 19, 2021 - - - -
Magidor-style embedding characterizations of large cardinals
Motivated by a classical theorem of Magidor, I will present results providing characterizations of important objects from the lower end of the large cardinal hierarchy through the existence of elementary embeddings between set-sized models that map their critical point to the large cardinal in question. Focusing on the characterization of shrewd cardinals, introduced by Rathjen in a proof-theoretic context, I will show how these results can be used in the study of the combinatorics of strong chain conditions and the investigation of principles of structural reflection formulated by Bagaria.
- - - - Monday, Feb 22, 2021 - - - -
- - - - Tuesday, Feb 23, 2021 - - - -
- - - - Wednesday, Feb 24, 2021 - - - -
- - - - Thursday, Feb 25, 2021 - - - -
- - - - Friday, Feb 26, 2021 - - - -
Farmer Schlutzenberg, University of Münster
(Non)uniqueness and (un)definability of embeddings beyond choice
Work in ZF and let j:Vα→Vα be an elementary, or partially elementary, embedding. One can examine the degree of uniqueness, definability or constructibility of j. For example, is there β<α such that j is the unique (partially) elementary extension of j↾Vβ? Is j definable from parameters over Vα? We will discuss some results along these lines, illustrating that answers can depend heavily on circumstances. Some of the work is due independently and earlier to Gabriel Goldberg.
- - - - Web Site - - - -
"Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)"
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Logic Seminar 17 Feb 2021 17:00 hrs at NUS by Xiao Ming
Upcoming CMU math logic events
Upcoming math logic events at CMU
This Week in Logic at CUNY
Logic and Metaphysics Workshop
Date: Monday, Feb 8, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu
Patrick Girard, Auckland
Title: Classical Counterpossibles
Abstract: We present four classical theories of counterpossibles that combine modalities and counterfactuals. Two theories are anti-vacuist and forbid vacuously true counterfactuals, two are quasi-vacuist and allow counterfactuals to be vacuously true when their antecedent is not only impossible, but also inconceivable. The theories vary on how they restrict the interaction of modalities and counterfactuals. We provide a logical cartography with precise acceptable boundaries, illustrating to what extent nonvacuism about counterpossibles can be reconciled with classical logic.
Note: this is joint work with Rohan French (UC Davis) and Dave Ripley (Monash).
- - - - Tuesday, Feb 9, 2021 - - - -
Leszek Kołodziejczyk, University of Warsaw
An isomorphism theorem for models of Weak Kőnig's Lemma without induction
We prove that any two countable models of the theory WKL∗0 sharing the same first-order universe and containing the same counterexample to Σ01 induction are isomorphic.
This theorem implies that over WKL∗0+¬IΣ01, the analytic hierarchy collapses to the arithmetic hierarchy. It also implies that WKL∗0 is the strongest Π12 statement that is Π11-conservative over RCA∗0+¬IΣ01. Together with the (slightly subtle) generalizations of the theorem to higher levels of the arithmetic hierarchy, this gives an 'almost negative' answer to a question of Towsner, who asked whether Π11-conservativity of Π12 sentences over collection principles is a Π02-complete computational problem. Our results also have some implications for the reverse mathematics of combinatorial principles: for instance, we get a specific Π11 sentence that is provable in RCA0+BΣ02 exactly if the Π11 consequences of RCA0+RT22 coincide with BΣ02.
On the side, we also give a positive answer to Towsner's question as originally stated.
Joint work with Marta Fiori Carones, Tin Lok Wong, and Keita Yokoyama.
- - - - Wednesday, Feb 10, 2021 - - - -
Date and Time: Wednesday February 10, 2021, 7:00 - 8:30 PM., on Zoom.
Title: Shuffling cards as an operad.
Abstract: The theory of how two packs of cards may be shuffled together to form a single pack has been remarkably well-studied in combinatorics, group theory, statistics, and other areas of mathematics. This talk aims to study natural extensions where 1/ We may have infinitely many cards in a deck, 2/ We may take the result of a previous shuffle as one of our decks of cards (i.e. shuffles are hierarchical), and 3/ There may even be an infinite number of decks of cards.
Far from being 'generalisation for generalisation's sake', the original motivation came from theoretical & practical computer science. The mathematics of card shuffles is commonly used to describe processing in multi-threaded computations. Moving to the infinite case gives a language in which one may talk about potentially non-terminating processes, or servers with an unbounded number of clients, etc.
However, this talk is entirely about algebra & category theory -- just as in the finite case, the mathematics is of interest in its own right, and should be studied as such.
We model shuffles using operads. The intuition behind them of allowing for arbitrary n-ary operations that compose in a hierarchical manner makes them a natural, inevitable choice for describing such processes such as merging multiple packs of cards.
We use very concrete examples, based on endomorphism operads in groupoids of arithmetic operations. The resulting structures are at the same time both simple (i.e. elementary arithmetic operations), and related to deep structures in mathematics and category theory (topologies, tensors, coherence, associahedra, etc.)
We treat this as a feature, not a bug, and use it to describe complex structures in elementary terms. We also aim to give previously unobserved connections between distinct areas of mathematics.
- - - - Thursday, Feb 11, 2021 - - - -
Philog Seminar
Thursday February 11, 6:30 PM
A Zoom link will be posted on philog.arthurpaulpedersen.org
Jayant Shah, Mathematics Department, Northeastern University
The Aumann Maschler paper on the Game theoretic analysis of a bankruptcy problem from the Talmud
- - - - Friday, Feb 12, 2021 - - - -
Indestructibility (or otherwise) of subcompactness and C(n)-supercompactness
Indestructibility results of large cardinals have been an area of interest since Laver's 1978 proof that the supercompactness of κ may be made indestructible by any <κ-directed closed forcing. I will present a continuation of this work, showing that α-subcompact cardinals may be made suitably indestructible, but that for C(n)-supercompact cardinals this is largely not possible.
- - - - Monday, Feb 15, 2021 - - - -
- - - - Tuesday, Feb 16, 2021 - - - -
Mateusz Łełyk, University of Warsaw
Nonequivalent axiomatizations of PA and the Tarski Boundary
We study a family of axioms expressing‘All axioms of PA are true.' (*)where PA denotes Peano Arithmetic. More precisely, each such axiom states that all axioms from a chosen axiomatization of PA are true. We start with a very natural theory of truth CT−(PA) which is a finite extension of PA in the language of arithmetic augmented with a fresh predicate T to serve as a truth predicate for the language of arithmetic. Additional axioms of this theory are straightforward translations of inductive Tarski truth conditions. To study various possible ways of expressing (*), we investigate extensions of CT−(PA) with axioms of the form∀x(δ(x)→T(x)).In the above (and throughout the whole abstract) δ(x) is an elementary formula which is proof-theoretically equivalent to the standard axiomatization of PA with the induction scheme, i.e. the equivalence∀x(Provδ(x)≡ProvPA(x)).is provable in IΣ1. For every such δ, the extension of CT−(PA) with the above axiom will be denoted CT−[δ].
In particular we shall focus on the arithmetical strength of theories CT−[δ]. The 'line' demarcating extensions of CT−(PA) which are conservative over PA from the nonconservative ones is known in the literature as the Tarski Boundary. For some time, there seemed to be the least (in terms of deductive strength) *natural* extension of CT−(PA) on the nonconservative side of the boundary, whose one axiomatization is given by CT−(PA) and Δ0 induction for the extended language (the theory is called CT0). This theory can equivalently be axiomatized by adding to CT−(PA) the natural formal representation of the statement 'All theorems of PA are true.'. We show that the situation between the Tarski Boundary and CT0 is much more interesting:
Theorem 1: For every r.e. theory Th in the language of arithmetic the following are equivalent:
1) CT0⊢ Th
2) there exists δ such that CT−[δ] and Th have the same arithmetical consequences.
Theorem 1 can be seen as a representation theorem for r.e. theories below REFω(PA) (all finite iterations of uniform reflection over PA, which is the set of arithmetical consequences of CT0): each such theory can be finitely axiomatized by a theory of the form CT−[δ], where δ is proof-theoretically reducible to PA.
Secondly, we use theories CT−[δ] to investigate the situation below the Tarski Boundary. We shall prove the following result
Theorem 2: There exists a family {δf}f∈ω<ω such that for all f,g∈ω<ω
1) CT−[δf] is conservative over PA;
2) if f⊊g, then CT−[δg] properly extends CT−[δf];
3) if f⊥g then CT−[δg]∪CT−[δf] is nonconservative over PA (but consistent).
- - - - Wednesday, Feb 17, 2021 - - - -
Title: Finiteness Spaces, Generalized Polynomial Rings and Topological Groupoids.
Abstract: The category of finiteness spaces was introduced by Thomas Ehrhard as a model of classical linear logic, where a set is equipped with a class of subsets to be thought of as finitary. Morphisms are relations preserving the finitary structure. The notion of finitary subset allows for a sharp analysis of computational structure.
Working with finiteness spaces forces the number of summands in certain calculations to be finite and thus avoid convergence questions. An excellent example of this is how Ribenboim’s theory of generalized power series rings can be naturally interpreted by assigning finiteness monoid structure to his partially ordered monoids. After Ehrhard’s linearization construction is applied, the resulting structures are the rings of Ribenboim’s construction.
There are several possible choices of morphism between finiteness spaces. If one takes structure-preserving partial functions, the resulting category is complete, cocomplete and symmetric monoidal closed. Using partial functions, we are able to model topological groupoids, when we consider composition as a partial function. We can associate to any hemicompact etale Hausdorff groupoid a complete convolution ring. This is in particular the case for the infinite paths groupoid associated to any countable row-finite directed graph.
- - - - Thursday, Feb 18, 2021 - - - -
- - - - Friday, Feb 19, 2021 - - - -
- - - - Web Site - - - -
"Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)"
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Barcelona Set theory Seminar
Talk by Andrés Villaveces tomorrow (1 30 pm)
Bio: Andrés Villaveces is a mathematician, working at Universidad Nacional de Colombia in Bogotá. Villaveces earned his doctoral degree from the University of Wisconsin-Madison in 1996 under the supervision of Ken Kunen. He held a postdoctoral position at the Hebrew University of Jerusalem (1996-1997) and has been a visiting professor at Carnegie Mellon University (2002-2003) and at the University of Helsinki (2007 and 2015). His work centers on the model theory of Abstract Elementary Classes and its connections with set theory and other parts of logic and mathematics.
Talk by Andrés Villaveces Friday ( 1 30 pm)
Bio: Andrés Villaveces is a mathematician, working at Universidad Nacional de Colombia in Bogotá. Villaveces earned his doctoral degree from the University of Wisconsin-Madison in 1996 under the supervision of Ken Kunen. He held a postdoctoral position at the Hebrew University of Jerusalem (1996-1997) and has been a visiting professor at Carnegie Mellon University (2002-2003) and at the University of Helsinki (2007 and 2015). His work centers on the model theory of Abstract Elementary Classes and its connections with set theory and other parts of logic and mathematics.
This Week in Logic at CUNY
- - - - Tuesday, Feb 2, 2021 - - - -
James Walsh, Cornell University
Reducing omega-model reflection to iterated syntactic reflection
Two types of principles are commonly called “reflection principles” in reverse mathematics. According to syntactic reflection principles for T, every theorem of T (from some complexity class) is true. According to semantic reflection principles, every set belongs to some (sufficiently correct) model of T. We will present a connection between syntactic reflection and semantic reflection in second-order arithmetic: for any Pi^1_2 axiomatized theory T, every set is contained in an omega model of T if and only if every iteration of Pi^1_1 reflection for T along a well-ordering is Pi^1_1 sound. There is a thorough proof-theoretic understanding of the latter in terms of ordinal analysis. Accordingly, these reductions yield proof-theoretic analyses of omega-model reflection principles. This is joint work with Fedor Pakhomov.
- - - - Wednesday, Feb 3, 2021 - - - -
Date and Time: Wednesday February 3, 2021, 7:00 - 8:30 PM., on Zoom.
Title: Isotropy Groups of Quasi-Equational Theories.
Abstract: In [2], my PhD supervisors (Pieter Hofstra and Philip Scott) and I studied the new topos-theoretic phenomenon of isotropy (as introduced in [1]) in the context of single-sorted algebraic theories, and we gave a logical/syntactic characterization of the isotropy group of any such theory, thereby showing that it encodes a notion of inner automorphism or conjugation for the theory. In the present talk, I will summarize the results of my recent PhD thesis, in which I build on this earlier work by studying the isotropy groups of (multi-sorted) quasi-equational theories (also known as essentially algebraic, cartesian, or finite limit theories). In particular, I will show how to give a logical/syntactic characterization of the isotropy group of any such theory, and that it encodes a notion of inner automorphism or conjugation for the theory. I will also describe how I have used this characterization to exactly characterize the ‘inner automorphisms’ for several different examples of quasi-equational theories, most notably the theory of strict monoidal categories and the theory of presheaves valued in a category of models. In particular, the latter example provides a characterization of the (covariant) isotropy group of a category of set-valued presheaves, which had been an open question in the theory of categorical isotropy.
[1] J. Funk, P. Hofstra, B. Steinberg. Isotropy and crossed toposes. Theory and Applications of Categories 26, 660-709, 2012.
[2] P. Hofstra, J. Parker, P.J. Scott. Isotropy of algebraic theories. Electronic Notes in Theoretical Computer Science 341, 201-217, 2018.
- - - - Thursday, Feb 4, 2021 - - - -
- - - - Friday, Feb 5, 2021 - - - -
Andreas Blass, University of Michigan
Choice from Finite Sets: A Topos View
Tarski proved (but didn't publish) the theorem that choice from pairs implies choice from four-element sets. Mostowski (1937) began a systematic study of such implications between choice axioms for families of finite sets. Gauntt (1970) completed that study (but didn't publish the results), obtaining equivalent characterizations in terms of fixed points of permutation groups. Truss (1973) extended Gauntt's results (and published this work).
It turns out that these finite choice axioms and their group-theoretic characterizations are instances of the same topos-theoretic statements, interpreted in two very different classes of topoi. My main result is an extension of that observation to the class of all topoi.
Most of my talk will be explaining the background: finite choice axioms, permutation groups, and a little bit about topoi - just enough to make sense of the main result. If time permits, I'll describe some of the ingredients of the proof.
- - - - Monday, Feb 8, 2021 - - - -
Logic and Metaphysics Workshop
Date: Monday, Feb 8, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu
Patrick Girard, Auckland
- - - - Tuesday, Feb 9, 2021 - - - -
Leszek Kołodziejczyk, University of Warsaw
An isomorphism theorem for models of Weak Kőnig's Lemma without induction
We prove that any two countable models of the theory WKL∗0 sharing the same first-order universe and containing the same counterexample to Σ01 induction are isomorphic.
This theorem implies that over WKL∗0+¬IΣ01, the analytic hierarchy collapses to the arithmetic hierarchy. It also implies that WKL∗0 is the strongest Π12 statement that is Π11-conservative over RCA∗0+¬IΣ01. Together with the (slightly subtle) generalizations of the theorem to higher levels of the arithmetic hierarchy, this gives an 'almost negative' answer to a question of Towsner, who asked whether Π11-conservativity of Π12 sentences over collection principles is a Π02-complete computational problem. Our results also have some implications for the reverse mathematics of combinatorial principles: for instance, we get a specific Π11 sentence that is provable in RCA0+BΣ02 exactly if the Π11 consequences of RCA0+RT22 coincide with BΣ02.
On the side, we also give a positive answer to Towsner's question as originally stated.
Joint work with Marta Fiori Carones, Tin Lok Wong, and Keita Yokoyama.
- - - - Wednesday, Feb 10, 2021 - - - -
Date and Time: Wednesday February 10, 2021, 7:00 - 8:30 PM., on Zoom.
Title: Invertibility in Operads : an elementary arithmetic approach.
Abstract: This talk is motivated by two areas of 'lost mathematics' -- topics where it is clear that interesting theory was once known & understood, but only incomplete traces remain in the historical record. One of these was due to ancient Greek mathematicians & logicians, and the other is a much lesser-known relation of a famous open problem from the 20th century.
One objective of this talk is to trace a link between the two. However, this is not an exercise in the 'History of Mathematics' -- the connections rely on theory that certainly was not understood in either time period.
Precisely, we consider 'Invertible Operads' -- that is, those whose composition operations are either partially or globally invertible. We look at examples that are freely generated by some given set of operations, with particular reference to those whose composition operations may be given by elementary arithmetic functions.
We demonstrate how such structures arise in a range of different topics, providing previously unobserved connections between them. This includes subjects such as standard Young tableaux, mixed-radix counting systems, topologies on the natural numbers, logical models, famous groups, and combinatorially-inspired polyhedra.
This is very much work in progress, and aims to present interesting questions as much as interesting structures and results.
- - - - Thursday, Feb 11, 2021 - - - -
- - - - Friday, Feb 12, 2021 - - - -
- - - - Other Logic News - - - -
- - - - Web Site - - - -
"Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)"
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Barcelona Set theory Seminar
CMU events starting next week
Tomorrow: Corey Switzer at 1 30 pm (Toronto Time)
Cardinal characteristics on the generalized Baire and Cantor spaces $\kappa^\kappa$ and $2^\kappa$ have recently generated significant interest. In this talk I will introduce a different generalization of cardinal characteristics, namely to the space of functions $f:\omega^\omega \to \omega^\omega$. Given an ideal $I$ on Baire space and a relation $R$ let us define $f R_I g$ for $f$ and $g$ functions from $\omega^\omega$ to $\omega^\omega$ if and only if $f(x) R g(x)$ for an $I$-measure one set of $x \in \omega^\omega$. By letting $I$ vary over the null ideal, the meager ideal and the bounded ideal; and $R$ vary over the relations $\leq^*$, $\neq^*$ and $\in^*$ we get 18 new cardinal characteristics by considering the bounding and dominating numbers for these relations. These new cardinals form a diagram of provable implications similar to the Cichoń diagram. They also interact in several surprising ways with the cardinal characteristics on $\omega$. For instance, they can be arbitrarily large in models of CH, yet they can be $\aleph_1$ in models where the continuum is arbitrarily large. They are bigger in the Sacks model than the Cohen model. I will introduce these cardinals, show some of the provable implications and discuss what is known about consistent inequalities, focusing on the $\mathfrak{b}$-numbers in well-known models such as the Cohen and Random model. This is joint work with Jörg Brendle.
Bio: Corey Bacal Switzer is currently a postdoctoral researcher at the Kurt Gödel Research Center For Mathematical Logic in the Mathematics Department of the University of Vienna working under Vera Fischer. He finished his PhD at the CUNY Graduate Center in New York in 2020. His research is in set theory, focusing on forcing, cardinal characteristics and infinite combinatorics
Logic Seminar 3 Feb 2021 17:00 hrs at NUS by Wong Tin Lok
Barcelona Set theory Seminar
(KGRC) research seminar talk on Thursday, January 28
This Friday Talk: Corey Switzer (usual time)
Cardinal characteristics on the generalized Baire and Cantor spaces $\kappa^\kappa$ and $2^\kappa$ have recently generated significant interest. In this talk I will introduce a different generalization of cardinal characteristics, namely to the space of functions $f:\omega^\omega \to \omega^\omega$. Given an ideal $I$ on Baire space and a relation $R$ let us define $f R_I g$ for $f$ and $g$ functions from $\omega^\omega$ to $\omega^\omega$ if and only if $f(x) R g(x)$ for an $I$-measure one set of $x \in \omega^\omega$. By letting $I$ vary over the null ideal, the meager ideal and the bounded ideal; and $R$ vary over the relations $\leq^*$, $\neq^*$ and $\in^*$ we get 18 new cardinal characteristics by considering the bounding and dominating numbers for these relations. These new cardinals form a diagram of provable implications similar to the Cichoń diagram. They also interact in several surprising ways with the cardinal characteristics on $\omega$. For instance, they can be arbitrarily large in models of CH, yet they can be $\aleph_1$ in models where the continuum is arbitrarily large. They are bigger in the Sacks model than the Cohen model. I will introduce these cardinals, show some of the provable implications and discuss what is known about consistent inequalities, focusing on the $\mathfrak{b}$-numbers in well-known models such as the Cohen and Random model. This is joint work with Jörg Brendle.
Bio: Corey Bacal Switzer is currently a postdoctoral researcher at the Kurt Gödel Research Center For Mathematical Logic in the Mathematics Department of the University of Vienna working under Vera Fischer. He finished his PhD at the CUNY Graduate Center in New York in 2020. His research is in set theory, focusing on forcing, cardinal characteristics and infinite combinatorics
This Week in Logic at CUNY
- - - - Monday, Jan 25, 2021 - - - -
- - - - Tuesday, Jan 26, 2021 - - - -
- - - - Wednesday, Jan 27, 2021 - - - -
- - - - Thursday, Jan 28, 2021 - - - -
- - - - Friday, Jan 29, 2021 - - - -
Erin Carmody, Fordham University
The relationships between measurable and strongly compact cardinals: Part II
This talk is about the ongoing investigation of the relationships between measurable and strongly compact cardinals. I will present some of the history of the theorems in this theme, including Magidor's identity crisis, and give new results. The theorems presented are in particular about the relationships between strongly compact cardinals and measurable cardinals of different Mitchell orders. One of the main theorems is that there is a universe where κ1 and κ2 are the first and second strongly compact cardinals, respectively, and where κ1 is least with Mitchell order 1, and κ2 is the least with Mitchell order 2. Another main theorem is that there is a universe where κ1 and κ2 are the first and second strongly compact cardinals, respectively, with κ1 the least measurable cardinal such that o(κ1)=2 and κ2 the least measurable cardinal above κ1. This is a joint work in progress with Victoria Gitman and Arthur Apter.
Next Week in Logic at CUNY:
- - - - Monday, Feb 1, 2021 - - - -
- - - - Tuesday, Feb 2, 2021 - - - -
James Walsh, Cornell University
Reducing omega-model reflection to iterated syntactic reflection
Two types of principles are commonly called “reflection principles” in reverse mathematics. According to syntactic reflection principles for T, every theorem of T (from some complexity class) is true. According to semantic reflection principles, every set belongs to some (sufficiently correct) model of T. We will present a connection between syntactic reflection and semantic reflection in second-order arithmetic: for any Pi^1_2 axiomatized theory T, every set is contained in an omega model of T if and only if every iteration of Pi^1_1 reflection for T along a well-ordering is Pi^1_1 sound. There is a thorough proof-theoretic understanding of the latter in terms of ordinal analysis. Accordingly, these reductions yield proof-theoretic analyses of omega-model reflection principles. This is joint work with Fedor Pakhomov.
- - - - Wednesday, Feb 3, 2021 - - - -
- - - - Thursday, Feb 4, 2021 - - - -
- - - - Friday, Feb 5, 2021 - - - -
- - - - Other Logic News - - - -
- - - - Web Site - - - -
"Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)"
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Two talks by B. Siskind on February 9
Tomorrow two talks (11 am and 1 30 pm)
These principles are at odds with each other. The former is a compactness type principle. (Compactness is the phenomenon where if a certain property holds for every smaller substructure of an object, then it holds for the entire object.) In contrast, failure of SCH is an instance of incompactness. The natural question is whether we can have both of these simultaneously. We show the answer is yes.
We describe a Prikry style iteration, and use it to force stationary reflection in the presence of not SCH. Then we obtain this situation at $\aleph_{\omega}$ . This is joint work with Alejandro Poveda and Assaf Rinot.
Abstract:
The search for universal models began in the early twentieth century when Hausdorff showed that there is a universal linear order of cardinality $\aleph_{n+1}$ if $2^{\aleph_n}= \aleph_{n + 1}$, i.e., a linear order $U$ of cardinality $\aleph_{n+1}$ such that every linear order of cardinality $\aleph_{n+1}$ embeds in $U$. In this talk, we will study universal models in several classes of abelian groups and modules with respect to pure embeddings. In particular, we will present a complete solution below $\aleph_\omega$, with the exception of $\aleph_0$ and $\aleph_1$, to Problem 5.1 in page 181 of \emph{Abelian Groups} by L\'{a}szl\'{o} Fuchs, which asks to find the cardinals $\lambda$ such that there is a universal abelian p-group for purity of cardinality $\lambda$. The solution presented will use both model-theoretic and set-theoretic ideas.
Two events on February 16
On Logic Seminar This Semester
(KGRC) research seminar talk on Thursday, January 21
Barcelona Set theory Seminar
BLAST 2021: June 9-13
Two events on February 2
Two talks next week (January 22nd)
Abstract: (In previous email)
Hello everyone,To start the semester we will have two talks: one at 11 am (Toronto time) and another at 1 30 pm (Toronto time).Please use the following link and fill the form (every week) to enter the meeting. This form helps the Field Institute to know statistical data about attendance.Here the speakers information:Speaker:Dima Sinapova, UIC, University of Illinois at Chicago, University of Illinois, ChicagoDate and Time: Friday, January 22, 2021 - 11am to 12:30pmLocation: OnlineAbstract:Two classical results of Magidor are: (1) from large cardinals it is consistent to have reflection at $\aleph_{\omega+1}$ and (2) from large cardinals it is consistent to have the failure of SCH at $\aleph_{\omega}$.These principles are at odds with each other. The former is a compactness type principle. (Compactness is the phenomenon where if a certain property holds for every smaller substructure of an object, then it holds for the entire object.) In contrast, failure of SCH is an instance of incompactness. The natural question is whether we can have both of these simultaneously. We show the answer is yes.
We describe a Prikry style iteration, and use it to force stationary reflection in the presence of not SCH. Then we obtain this situation at $\aleph_{\omega}$ . This is joint work with Alejandro Poveda and Assaf Rinot.
Speaker: Marcos Mazari Armida, Carnagie Mellon University
Date and Time: Friday, January 22, 2021 - 11am to 12:30pmTitle: Universal models in classes of abelian groups and modules
Abstract:
The search for universal models began in the early twentieth century when Hausdorff showed that there is a universal linear order of cardinality $\aleph_{n+1}$ if $2^{\aleph_n}= \aleph_{n + 1}$, i.e., a linear order $U$ of cardinality $\aleph_{n+1}$ such that every linear order of cardinality $\aleph_{n+1}$ embeds in $U$. In this talk, we will study universal models in several classes of abelian groups and modules with respect to pure embeddings. In particular, we will present a complete solution below $\aleph_\omega$, with the exception of $\aleph_0$ and $\aleph_1$, to Problem 5.1 in page 181 of \emph{Abelian Groups} by L\'{a}szl\'{o} Fuchs, which asks to find the cardinals $\lambda$ such that there is a universal abelian p-group for purity of cardinality $\lambda$. The solution presented will use both model-theoretic and set-theoretic ideas.Iván Ongay Valverde (he/his)My email account ongay@math.wisc.edu will be closed in October 2020. Please contact me either at ongay@yorku.ca or at ivan.ongay.valverde@gmail.com
Two talks next week (January 22nd)
These principles are at odds with each other. The former is a compactness type principle. (Compactness is the phenomenon where if a certain property holds for every smaller substructure of an object, then it holds for the entire object.) In contrast, failure of SCH is an instance of incompactness. The natural question is whether we can have both of these simultaneously. We show the answer is yes.
We describe a Prikry style iteration, and use it to force stationary reflection in the presence of not SCH. Then we obtain this situation at $\aleph_{\omega}$ . This is joint work with Alejandro Poveda and Assaf Rinot.
Abstract:
The search for universal models began in the early twentieth century when Hausdorff showed that there is a universal linear order of cardinality $\aleph_{n+1}$ if $2^{\aleph_n}= \aleph_{n + 1}$, i.e., a linear order $U$ of cardinality $\aleph_{n+1}$ such that every linear order of cardinality $\aleph_{n+1}$ embeds in $U$. In this talk, we will study universal models in several classes of abelian groups and modules with respect to pure embeddings. In particular, we will present a complete solution below $\aleph_\omega$, with the exception of $\aleph_0$ and $\aleph_1$, to Problem 5.1 in page 181 of \emph{Abelian Groups} by L\'{a}szl\'{o} Fuchs, which asks to find the cardinals $\lambda$ such that there is a universal abelian p-group for purity of cardinality $\lambda$. The solution presented will use both model-theoretic and set-theoretic ideas.
(KGRC) research seminar talk on Thursday, January 14
Barcelona Set theory Seminar
Logic Seminar at NUS on Wednesday 13 Jan 2021 17:00 hrs - World Logic Day Special
(KGRC) research seminar talk on Thursday, December 17
Barcelona Set Theory Seminar
This Week in Logic at CUNY
Best,
Logic and Metaphysics Workshop
Shay Logan (Kansas State)
Federico Pailos (Buenos Aires)
Dave Ripley (Monash)
Chris Scambler (NYU)
We may go on somewhat longer than the usual two hours if the discussion is productive. The meeting is open to all interested.
- - - - Tuesday, Dec 15, 2020 - - - -
- - - - Wednesday, Dec 16, 2020 - - - -
Speaker: Arthur Parzygnat, IHES.
Date and Time: Wednesday December 16, 2020, 1:00 - 2:30 PM. ***NOTICE THE SPECIAL TIME***, on Zoom.
Title: A functorial characterization of classical and quantum entropies.
Abstract: Entropy appears as a useful concept in a wide variety of academic disciplines. As such, one would suspect that category theory would provide a suitable language to encompass all or most of these definitions. The Shannon entropy has recently been given a characterization as a certain affine functor by Baez, Fritz, and Leinster. This characterization is the only characterization I know of that uses linear assumptions (as opposed to additive, exponential, logarithmic, etc). Here, we extend that characterization to include the von Neumann entropy as well as highlight the new categorical structures that arise when trying to do so. In particular, we introduce Grothendieck fibrations of convex categories, and we review the notion of a disintegration, which is a key part of conditional probability and Bayesian statistics and plays a crucial role in our characterization theorem. The characterization of Baez, Fritz, and Leinster interprets Shannon entropy in terms of the information loss associated to a deterministic process, which is possible since the entropy difference associated to such a process is always non-negative. This fails for quantum entropy, and has important physical consequences.
References:
Paper (and references therein)
Paper (original paper of Baez, Fritz, and Leinster)
- - - - Thursday, Dec 17, 2020 - - - -
Philog Seminar
Thursday, December 17, 6:30 PM EST
Barbara H. Partee, Department of Linguistics, University of Massachusetts Amherst
Language and Logic: Ideas and Controversies in the History of Formal Semantics
(As a very senior and accomplished linguist she is the right person to tell us about formal semantics.)
Brief abstract: The history of formal semantics and pragmatics over the last 50 years is a story of collaboration among linguists, logicians, and philosophers. Since this talk is for a seminar in philosophy, logic, and games, and I’m a linguist, I’ll emphasize aspects of the pre-history and history of formal semantics that concern the relation between language and logic, not presupposing knowledge of linguistics.
Zoom link will be posted on https://philog.arthurpaulpedersen.org/
- - - - Friday, Dec 18, 2020 - - - -
- - - - Monday, Dec 21, 2020 - - - -
- - - - Tuesday, Dec 22, 2020 - - - -
- - - - Wednesday, Dec 23, 2020 - - - -
- - - - Thursday, Dec 24, 2020 - - - -
- - - - Friday, Dec 25, 2020 - - - -
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)
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(KGRC) research seminar talk on Thursday, December 10
This Week in Logic at CUNY
- - - - Monday, Dec 7, 2020 - - - -
Logic and Metaphysics Workshop
Date: Monday, December 7, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu
Jennifer McDonald (CUNY)
Abstract: A promising account of actual causation – the causal relation holding between two token events – uses the language of structural equation models (SEMs). Such an account says, roughly, that actual causation holds between two token events when there is a suitable model according to which (1) the two events occur; and (2) intervening on the model to change the value of the variable that represents the cause changes the value of the variable that represents the effect (Halpern & Pearl, 2005; Hitchcock, 2001; Weslake, 2015; Woodward, 2003). Of course, this calls for an account of when a model is suitable – or, apt. Although initially bracketed, this issue is increasingly pressing; in part due to the recently discovered problem of structural isomorphs (Hall 2007; Hitchcock 2007a; Blanchard and Schaffer 2017; Menzies 2017). This paper offers a unified analysis of two aptness requirements from the literature – those enjoining us to include essential structure and avoid unstable models. While successfully invoked by Blanchard and Schaffer (2017) to resolve the problem of structural isomorphs, these requirements are unilluminating as they stand. My paper synthesizes them into a single aptness requirement that, I claim, gets to the heart of what’s representationally required of a causal model for capturing actual causation.
- - - - Tuesday, Dec 8, 2020 - - - -
- - - - Wednesday, Dec 9, 2020 - - - -
Models of Peano Arithmetic (MOPA)
The seminar will take place virtually at 3pm US Eastern Standard Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Konrad Zdanowski, Cardinal Stefan Wyszynski University in Warsaw
Truth predicate for Δ0 formulas and PSPACE computations
We consider a bounded arithmetic in Buss's language enriched with a predicate Tr which is assumed to be a truth definition for bounded sentences. Among other things we assume polynomial induction for Σb1(Tr) formulas. We show that such an arithmetic captures PSPACE. We prove a witnessing theorem for such an arithmetic by an interpretation of free-cuts free proofs of strict Σ1,b1 in U1,∗2, a canonical second order arithmetic capturing PSPACE. It follows that the problem of the existence of a truth definition for Δ0 sentences without the totality of exp might be more about separating subexponential time alternation hierarchies from PSPACE.
The presentation is based on the following article: Konrad Zdanowski, Truth definition for Δ0 formulas and PSPACE computations, Fundamenta Mathematicae 252(2021) , 1-38.
Date and Time: Wednesday December 9, 2020, 7:00 - 8:30 PM., on Zoom.
Title: Functorial Manifold Learning and Overlapping Clustering.
- - - - Thursday, Dec 10, 2020 - - - -
- - - - Friday, Dec 11, 2020 - - - -
Iteration, reflection, and singular cardinals
There is an inherent tension between stationary reflection and the failure of the singular cardinal hypothesis (SCH). The former is a compactness type principle that follows from large cardinals. Compactness is the phenomenon where if a certain property holds for every smaller substructure of an object, then it holds for the entire object. In contrast, failure of SCH is an instance of incompactness.
Two classical results of Magidor are:
(1) from large cardinals it is consistent to have reflection at ℵω+1, and
(2) from large cardinals it is consistent to have the failure of SCH at ℵω.
As these principles are at odds with each other, the natural question is whether we can have both. We show the answer is yes.
We describe a Prikry style iteration, and use it to force stationary reflection in the presence of not SCH. Then we obtain this situation at ℵω by interleaving collapses. This is joint work with Alejandro Poveda and Assaf Rinot.
- - - - Monday, Dec 14, 2020 - - - -
- - - - Tuesday, Dec 15, 2020 - - - -
- - - - Wednesday, Dec 16, 2020 - - - -
Speaker: Arthur Parzygnat, IHES.
Date and Time: Wednesday December 16, 2020, 1:00 - 2:30 PM. ***NOTICE THE SPECIAL TIME***, on Zoom.
Title: A functorial characterization of classical and quantum entropies.
Abstract: Entropy appears as a useful concept in a wide variety of academic disciplines. As such, one would suspect that category theory would provide a suitable language to encompass all or most of these definitions. The Shannon entropy has recently been given a characterization as a certain affine functor by Baez, Fritz, and Leinster. This characterization is the only characterization I know of that uses linear assumptions (as opposed to additive, exponential, logarithmic, etc). Here, we extend that characterization to include the von Neumann entropy as well as highlight the new categorical structures that arise when trying to do so. In particular, we introduce Grothendieck fibrations of convex categories, and we review the notion of a disintegration, which is a key part of conditional probability and Bayesian statistics and plays a crucial role in our characterization theorem. The characterization of Baez, Fritz, and Leinster interprets Shannon entropy in terms of the information loss associated to a deterministic process, which is possible since the entropy difference associated to such a process is always non-negative. This fails for quantum entropy, and has important physical consequences.
References:
Paper (and references therein)
Paper (original paper of Baez, Fritz, and Leinster)
- - - - Thursday, Dec 17, 2020 - - - -
- - - - Friday, Dec 18, 2020 - - - -
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)
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Barcelona Set Theory Seminar
Set theory in the UK workshop, online, December 4
Talk this Friday 2 hours-long (1 30 pm Toronto time)
location: Online
Please use the following link and fill the form (every week) to enter
the meeting. This form helps the Field Institute to know statistical
data about attendance.
https://zoom.us/meeting/register/tJUvcO2tqTMqEtdESHljnD_Ee4rneqRCkDqo
Speaker: Thomas Daniells Gilton
Affiliation: Department of Mathematics, The University of Pittsburgh
Title: The Abraham-Rubin-Shelah Open Coloring Axiom with a Large
Continuum
Abstract:
Open Coloring Axioms may be viewed as consistent generalizations of
Ramsey's Theorem to $\omega_1$ in which topological restrictions are
placed on the colorings. The first of these, denoted
$\mathsf{OCA}_{ARS}$, appeared in the 1985 paper by Abraham, Rubin, and
Shelah. There the authors showed that $\mathsf{OCA}_{ARS}$ is consistent
with $\mathsf{ZFC}$. To ensure that the posets which add the homogeneous
sets satisfy the c.c.c., they construct a type of ``diagonalization"
object (for a continuous coloring $\chi$) called a \emph{Preassignment
of Colors}, which guides the forcing to add the $\chi$-homogeneous sets.
However, the only known constructions of effective preassignments
require the $\mathsf{CH}$. Since a forcing iteration of $\aleph_1$-sized
posets all of whose proper initial segments satisfy the $\mathsf{CH}$
results in a model in which $2^{\aleph_0}$ is at most $\aleph_2$, this
leads naturally to the question of whether $\mathsf{OCA}_{ARS}$ is
consistent, say, with $2^{\aleph_0}=\aleph_3$.
In joint work with Itay Neeman, we answer this question in the
affirmative. In light of the $\mathsf{CH}$ obstacle, we only construct
names for preassignments with respect to a small class $\mathcal{A}$ of
$\mathsf{CH}$-preserving iterations. However, our preassignments are
powerful enough to work even over models in which the $\mathsf{CH}$
fails.
Our final forcing is built by combining the members of $\mathcal{A}$
into a new type of forcing, called a \emph{Partition Product}. A
partition product is a type of restricted memory iteration with
isomorphism and coherent-overlap conditions on the memories. In
particular, each ``memory" is isomorphic to a member of $\mathcal{A}$.
In this talk, we will describe in some detail the definition of a
Partition Product. We will then discuss how to construct more general
preassignments than those used by Abraham, Rubin, and Shelah, gesturing
at the end towards the full construction which we use for our theorem.
========================================
Speaker Bio:
I am a Visiting Assistant Professor in the department of Mathematics at
the University of Pittsburgh, having graduated from UCLA in the Fall of
2019 under the supervision of Itay Neeman. I am interested in questions
about what combinatorial principles determine the size of the continuum,
as well as in questions about the tension between compactness and
incompactness principles in set theory. I reside in Pittsburgh with my
wife, Marian (who is a philosopher of physics), with our indefatigable
toddler Zoe, and with our two cats.
(KGRC) research seminar talk on December 3
This Week in Logic at CUNY
Logic and Metaphysics Workshop
Date: Monday, November 23, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu
Behnam Zolghadr (LMU Munich)
Abstract: Similar to Meinong, Abū Hāšim al-Ǧubbāī (d.933), an Islamic theologian/philosopher, held the view that some objects do not exist. This paper is a comparative study between Meinong’s object theory and Abū Hāšim’s theory of nonexistent objects. Our comparative study will be carried out through three main topics: the characterization principle, objecthood, and the ontological status of existence itself. Moreover, Abū Hāšim and his followers argue that the view that some objects do not exist implies some truth value gaps and/or gluts. We will also discuss two of these arguments.
- - - - Tuesday, Nov 24, 2020 - - - -
Ask Sergei Artemov for the (usual) link, unless you already have it.
Speaker: Stepan Kuznetsov, Steklov Mathematical Institute, Russian Academy of SciencesTitle: Ad hoc algebraic models for non-standard Kleene stars
Abstract: Kleene iteration, or Kleene star, is one of the most intriguing algebraic operations appearing in theoretical computer science. In most conventional models, the Kleene star a* is interpreted as the union (limit) of n-th powers of a. In relational structures, this corresponds to reflexive-transitive closure, in language models it is iteration of languages, and so on. Such interpretation of the Kleene star is called *-continuous. However, the usual axiomatization of the Kleene star using induction principles (as opposed to the omega-rule), is essentially weaker and, thus, admits a broader class of models. Existence of nonstandard, non-*-continuous models can be easily proved non-constructively. However, in order to use such models for studying substructural logics with Kleene star one has to construct them explicitly. In this talk, we show two of such models, constructed for proving some facts about derivability in extensions of the Lambek calculus with the Kleene star. Both models are ad hoc algebraic constructions, and we do not yet know whether they could fit in a natural family of models.
- - - - Wednesday, Nov 25, 2020 - - - -
- - - - Thursday, Nov 26, 2020 - - - -
THANKSGIVING RECESS
- - - - Friday, Nov 27, 2020 - - - -
- - - - Monday, Nov 30, 2020 - - - -
Logic and Metaphysics Workshop
Date: Monday, November 30, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu
Abstract: In Reference without Referents, Mark Sainsbury aims to provide an account of reference that honours the common-sense view that sentences containing empty names like “Sherlock Holmes”, “Vulcan”, and “Santa Claus” are entirely intelligible, and that many such sentences — “Vulcan doesn’t exist”, “Many children believe that Santa Claus will give them presents at Christmas”, etc.— are literally true. Sainsbury’s account endorses the Davidsonian program in the theory of meaning, and combines this with a commitment to Negative Free Logic, which holds that all simple sentences containing empty names are false. In my talk, I pose a number of problems for this account. In particular, I question the ability of Negative Free Logic to make appropriate sense of the truth of familiar sentences containing empty names, including negative existential claims like “Vulcan doesn’t exist”.
Note: this is based on joint work with Frederick Kroon (Auckland).
- - - - Tuesday, Dec 1, 2020 - - - -
Ask Sergei Artemov for the (usual) link, unless you already have it.
Speaker: Rohit Parikh, Brooklyn College and CUNY Graduate Center
Title: TOPOLOGY AND EPISTEMIC LOGIC
Abstract. We present the main ideas behind a number of logical systems for reasoning about points and sets that incorporate knowledge-theoretic ideas, and also the main results about them. Some of our discussions will be about applications of modal ideas to topology, and some will be on applications of topological ideas in modal logic, especially in epistemic logic.
In the former area, we would like to present the basic ideas and results of topologic, the study of two-sorted bimodal logical systems interpreted on subset spaces; these are arbitrary sets with collections of subsets called opens. Many of the papers in this field deal with questions of axiomatizing the logics of particular classes of subset spaces determined by conditions on the “opens”, such as being closed under intersection, being topologies, or satisfying various chain conditions.
Work in this area has been done by RP as well as Larry Moss (Indiana), Andrew Dabrowski (Indiana), K Georgatos (CUNY), Angela Weiss (CUNY), Chris Steinsvold (CUNY), Bernhard Heinemann (Hagen), Can Baskent (CUNY) and many others.
Title: TOPOLOGY AND EPISTEMIC LOGIC
In the former area, we would like to present the basic ideas and results of topologic, the study of two-sorted bimodal logical systems interpreted on subset spaces; these are arbitrary sets with collections of subsets called opens. Many of the papers in this field deal with questions of axiomatizing the logics of particular classes of subset spaces determined by conditions on the “opens”, such as being closed under intersection, being topologies, or satisfying various chain conditions.
Work in this area has been done by RP as well as Larry Moss (Indiana), Andrew Dabrowski (Indiana), K Georgatos (CUNY), Angela Weiss (CUNY), Chris Steinsvold (CUNY), Bernhard Heinemann (Hagen), Can Baskent (CUNY) and many others.
- - - - Wednesday, Dec 2, 2020 - - - -
- - - - Thursday, Dec 3, 2020 - - - -
- - - - Friday, Dec 4, 2020 - - - -
- - - - Monday, Dec 7, 2020 - - - -
Logic and Metaphysics Workshop
Date: Monday, December 7, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu
Jennifer McDonald (CUNY)
Abstract: A promising account of actual causation – the causal relation holding between two token events – uses the language of structural equation models (SEMs). Such an account says, roughly, that actual causation holds between two token events when there is a suitable model according to which (1) the two events occur; and (2) intervening on the model to change the value of the variable that represents the cause changes the value of the variable that represents the effect (Halpern & Pearl, 2005; Hitchcock, 2001; Weslake, 2015; Woodward, 2003). Of course, this calls for an account of when a model is suitable – or, apt. Although initially bracketed, this issue is increasingly pressing; in part due to the recently discovered problem of structural isomorphs (Hall 2007; Hitchcock 2007a; Blanchard and Schaffer 2017; Menzies 2017). This paper offers a unified analysis of two aptness requirements from the literature – those enjoining us to include essential structure and avoid unstable models. While successfully invoked by Blanchard and Schaffer (2017) to resolve the problem of structural isomorphs, these requirements are unilluminating as they stand. My paper synthesizes them into a single aptness requirement that, I claim, gets to the heart of what’s representationally required of a causal model for capturing actual causation.
- - - - Tuesday, Dec 8, 2020 - - - -
- - - - Wednesday, Dec 9, 2020 - - - -
- - - - Thursday, Dec 10, 2020 - - - -
- - - - Friday, Dec 11, 2020 - - - -
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
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Barcelona Set Theory Seminar
Reminder: Talk tomorrow at 1 30
The study of inner models was initiated by Gödel’s analysis of the constructible universe L
. Later, it became necessary to study canonical inner models with large cardinals, e.g. measurable cardinals, strong cardinals or Woodin cardinals, which were introduced by Jensen, Mitchell, Steel, and others. Around the same time, the study of infinite two-player games was driven forward by Martin’s proof of analytic determinacy from a measurable cardinal, Borel determinacy from ZFC, and Martin and Steel’s proof of levels of projective determinacy from Woodin cardinals with a measurable cardinal on top. First Woodin and later Neeman improved the result in the projective hierarchy by showing that in fact the existence of a countable iterable model, a mouse, with Woodin cardinals and a top measure suffices to prove determinacy in the projective hierarchy.
This opened up the possibility for an optimal result stating the equivalence between local determinacy hypotheses and the existence of mice in the projective hierarchy, just like the equivalence of analytic determinacy and the existence of x♯
for every real xwhich was shown by Martin and Harrington in the 70’s. The existence of mice with Woodin cardinals and a top measure from levels of projective determinacy was shown by Woodin in the 90’s. Together with his earlier and Neeman’s results this estabilishes a tight connection between descriptive set theory in the projective hierarchy and inner model theory.
In this talk, we will outline some of the main results connecting determinacy hypotheses with the existence of mice with large cardinals and discuss a number of more recent results in this area.
On Friday Dec. 4th we will have Thomas Gilton. Please, also see the webpage http://www.fields.utoronto.ca/activities/20-21/set-theory-seminar
Sandra Muller Talk this Friday 1 30 pm
The study of inner models was initiated by Gödel’s analysis of the constructible universe L
. Later, it became necessary to study canonical inner models with large cardinals, e.g. measurable cardinals, strong cardinals or Woodin cardinals, which were introduced by Jensen, Mitchell, Steel, and others. Around the same time, the study of infinite two-player games was driven forward by Martin’s proof of analytic determinacy from a measurable cardinal, Borel determinacy from ZFC, and Martin and Steel’s proof of levels of projective determinacy from Woodin cardinals with a measurable cardinal on top. First Woodin and later Neeman improved the result in the projective hierarchy by showing that in fact the existence of a countable iterable model, a mouse, with Woodin cardinals and a top measure suffices to prove determinacy in the projective hierarchy.
This opened up the possibility for an optimal result stating the equivalence between local determinacy hypotheses and the existence of mice in the projective hierarchy, just like the equivalence of analytic determinacy and the existence of x♯
for every real xwhich was shown by Martin and Harrington in the 70’s. The existence of mice with Woodin cardinals and a top measure from levels of projective determinacy was shown by Woodin in the 90’s. Together with his earlier and Neeman’s results this estabilishes a tight connection between descriptive set theory in the projective hierarchy and inner model theory.
In this talk, we will outline some of the main results connecting determinacy hypotheses with the existence of mice with large cardinals and discuss a number of more recent results in this area.
On Friday Dec. 4th we will have Thomas Gilton. Please, also see the webpage http://www.fields.utoronto.ca/activities/20-21/set-theory-seminar
(KGRC) research seminar talk on Thursday, November 26
This Week in Logic at CUNY
Logic and Metaphysics Workshop
Date: Monday, November 23, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu
Behnam Zolghadr (LMU Munich)
Abstract: Similar to Meinong, Abū Hāšim al-Ǧubbāī (d.933), an Islamic theologian/philosopher, held the view that some objects do not exist. This paper is a comparative study between Meinong’s object theory and Abū Hāšim’s theory of nonexistent objects. Our comparative study will be carried out through three main topics: the characterization principle, objecthood, and the ontological status of existence itself. Moreover, Abū Hāšim and his followers argue that the view that some objects do not exist implies some truth value gaps and/or gluts. We will also discuss two of these arguments.
- - - - Tuesday, Nov 24, 2020 - - - -
Ask Sergei Artemov for the (usual) link, unless you already have it.
Speaker: Stepan Kuznetsov, Steklov Mathematical Institute, Russian Academy of SciencesTitle: Ad hoc algebraic models for non-standard Kleene stars
Abstract: Kleene iteration, or Kleene star, is one of the most intriguing algebraic operations appearing in theoretical computer science. In most conventional models, the Kleene star a* is interpreted as the union (limit) of n-th powers of a. In relational structures, this corresponds to reflexive-transitive closure, in language models it is iteration of languages, and so on. Such interpretation of the Kleene star is called *-continuous. However, the usual axiomatization of the Kleene star using induction principles (as opposed to the omega-rule), is essentially weaker and, thus, admits a broader class of models. Existence of nonstandard, non-*-continuous models can be easily proved non-constructively. However, in order to use such models for studying substructural logics with Kleene star one has to construct them explicitly. In this talk, we show two of such models, constructed for proving some facts about derivability in extensions of the Lambek calculus with the Kleene star. Both models are ad hoc algebraic constructions, and we do not yet know whether they could fit in a natural family of models.
- - - - Wednesday, Nov 25, 2020 - - - -
- - - - Thursday, Nov 26, 2020 - - - -
THANKSGIVING RECESS
- - - - Friday, Nov 27, 2020 - - - -
- - - - Monday, Nov 30, 2020 - - - -
Logic and Metaphysics Workshop
Date: Monday, November 30, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu
Abstract: In Reference without Referents, Mark Sainsbury aims to provide an account of reference that honours the common-sense view that sentences containing empty names like “Sherlock Holmes”, “Vulcan”, and “Santa Claus” are entirely intelligible, and that many such sentences — “Vulcan doesn’t exist”, “Many children believe that Santa Claus will give them presents at Christmas”, etc.— are literally true. Sainsbury’s account endorses the Davidsonian program in the theory of meaning, and combines this with a commitment to Negative Free Logic, which holds that all simple sentences containing empty names are false. In my talk, I pose a number of problems for this account. In particular, I question the ability of Negative Free Logic to make appropriate sense of the truth of familiar sentences containing empty names, including negative existential claims like “Vulcan doesn’t exist”.
Note: this is based on joint work with Frederick Kroon (Auckland).
- - - - Tuesday, Dec 1, 2020 - - - -
- - - - Wednesday, Dec 2, 2020 - - - -
- - - - Thursday, Dec 3, 2020 - - - -
- - - - Friday, Dec 4, 2020 - - - -
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Barcelona Set Theory Seminar
Reminder of tomorrow's talk 1 30 pm
Wadge theory provides an exhaustive analysis of the topological complexity of the subsets of a zero-dimensional Polish space. Fons van Engelen pioneered its applications to topology by obtaining a classification of the zero-dimensional homogeneous Borel spaces (recall that a space X is homogeneous if for all x,y∈X there exists a homeomorphism h:X⟶X such that h(x)=y).
As a corollary, he showed that all such spaces (apart from trivial exceptions) are in fact strongly homogeneous (recall that a space X is strongly homogeneous if all non-empty clopen subspaces of X are homeomorphic to each other).
In a joint work with the other members of the “Wadge Brigade” (namely, Raphaël Carroy and Sandra Müller), we showed that this last result extends beyond the Borel realm if one assumes AD. We intend to sketch the proof of this theorem, with a view towards a complete classification of the zero-dimensional homogeneous spaces under AD.
Andrea Medina talk-Toronto Set Theory Seminar
Wadge theory provides an exhaustive analysis of the topological complexity of the subsets of a zero-dimensional Polish space. Fons van Engelen pioneered its applications to topology by obtaining a classification of the zero-dimensional homogeneous Borel spaces (recall that a space X is homogeneous if for all x,y∈X there exists a homeomorphism h:X⟶X such that h(x)=y).
As a corollary, he showed that all such spaces (apart from trivial exceptions) are in fact strongly homogeneous (recall that a space X is strongly homogeneous if all non-empty clopen subspaces of X are homeomorphic to each other).
In a joint work with the other members of the “Wadge Brigade” (namely, Raphaël Carroy and Sandra Müller), we showed that this last result extends beyond the Borel realm if one assumes AD. We intend to sketch the proof of this theorem, with a view towards a complete classification of the zero-dimensional homogeneous spaces under AD.
(KGRC) research seminar talk on Thursday, November 19
This Week in Logic at CUNY
Logic and Metaphysics Workshop
Date: Monday, November 16, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu
Title: Hegel’s Logic as Logic and as Metaphysics
Abstract: In the Encyclopaedia Logic Hegel claims that logic “coincides with” metaphysics (§24). In this talk, I will explain why Hegelian logic (the science of thinking) is identical with metaphysics (the science of being). Along the way, I will also shed light on two of the most obscure aspects of Hegel’s logic: that it involves “movement” and that this movement works by the identification, and resolution, of contradictions.
- - - - Tuesday, Nov 17, 2020 - - - -
Computational Logic Seminar: no meeting on Tuesday November 17
http://lp2020.mi-ras.ru/open_lectures/
http://www.math.nsc.ru/conference/malmeet/20/Main.htm
- - - - Wednesday, Nov 18, 2020 - - - -
Speaker: Enrico Ghiorzi, Appalachian State University.
Date and Time: Wednesday November 18, 2020, 7:00 - 8:30 PM., on Zoom.
Title: Internal enriched categories.
- - - - Thursday, Nov 19, 2020 - - - -
- - - - Friday, Nov 20, 2020 - - - -
Philipp Schlicht University of Vienna
The recognisable universe in the presence of measurable cardinals
A set x of ordinals is called recognisable if it is defined, as a singleton, by a formula phi(y) with ordinal parameters that is evaluated in L[y]. The evaluation is always forcing absolute, in contrast to even Sigma_1-formulas with ordinal parameters evaluated in V. Furthermore, this notion is closely related to similar concepts in infinite computation and Hamkins' and Leahy's implicitly definable sets.
It is conjectured that the recognisable universe generated by all recognisable sets is forcing absolute, given sufficient large cardinals. Our goal is thus to determine the recognisable universe in the presence of large cardinals. The new main result, joint with Philip Welch, is a computation of the recognisable universe within the least inner model with infinitely many measurable cardinals.
- - - - Monday, Nov 23, 2020 - - - -
Logic and Metaphysics Workshop
Date: Monday, November 23, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu
Behnam Zolghadr (LMU Munich)
Abstract: Similar to Meinong, Abū Hāšim al-Ǧubbāī (d.933), an Islamic theologian/philosopher, held the view that some objects do not exist. This paper is a comparative study between Meinong’s object theory and Abū Hāšim’s theory of nonexistent objects. Our comparative study will be carried out through three main topics: the characterization principle, objecthood, and the ontological status of existence itself. Moreover, Abū Hāšim and his followers argue that the view that some objects do not exist implies some truth value gaps and/or gluts. We will also discuss two of these arguments.
- - - - Tuesday, Nov 24, 2020 - - - -
- - - - Wednesday, Nov 25, 2020 - - - -
- - - - Thursday, Nov 26, 2020 - - - -
THANKSGIVING RECESS
- - - - Friday, Nov 27, 2020 - - - -
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Barcelona Set Theory Seminar
Error in Zoom link (seminar tomorrow 11 am)
Toronto Set Theory Seminar 11 am (local time) tomorrow Friday 13th
11:00 am
Ralf Schindler (University of Münster, Germany)
Title: Martin's Maximum^++ implies the P_max axiom (*).
Abstract: Forcing axioms spell out the dictum that if a statement can be
forced, then it is already true. The P_max axiom (*) goes beyond that by
claiming that if a statement is consistent, then it is already true.
Here, the statement in question needs to come from a resticted class of
statements, and "consistent" needs to mean "consistent in a strong
sense." It turns out that (*) is actually equivalent to a forcing axiom,
and the proof is by showing that the (strong) consistency of certain
theories gives rise to a corresponding notion of forcing producing a
model of that theory. This is joint work with D. Asperó building upon
earlier work of R. Jensen and (ultimately) Keisler's "consistency
properties."
(KGRC) research seminar talk on Thursday, November 12
This Week in Logic at CUNY
Logic and Metaphysics Workshop
Date: Monday, November 9, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu
Eoin Moore (CUNY)
Title: Towards a Justification Logic for FDE
Abstract: In this work-in-progress, I aim to develop a justification logic counterpart to first degree entailment. I produce a logic which is an extension of FDE using justification terms. The results are extended to other paraconsistent logics.
- - - - Tuesday, Nov 10, 2020 - - - -
Algebraically, the IEL^- modality is a prenucleus operator widespread in the theory of locales and point-free topology. We consider predicate extensions of IEL^- (and some similar logics) and provide a sort of Kripke-Joyal semantics for those logics developing several ideas by R. Goldblatt. We show that such intuitionistic predicate modal logics are complete with respect to their cover systems with the Dedekind-MacNeille completion and the representation of Heyting algebras with corresponding operators.
- - - - Wednesday, Nov 11, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, Nov 11, 12:00pm
The seminar will take place virtually at 12pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Joel David Hamkins, Oxford University
Continuous models of arithmetic
Ali Enayat had asked whether there is a model of Peano arithmetic (PA) that can be represented as ⟨Q,⊕,⊗⟩, where ⊕ and ⊗ are continuous functions on the rationals Q. We prove, affirmatively, that indeed every countable model of PA has such a continuous presentation on the rationals. More generally, we investigate the topological spaces that arise as such topological models of arithmetic. The reals R, the reals in any finite dimension Rn, the long line and the Cantor space do not, and neither does any Suslin line; many other spaces do; the status of the Baire space is open.
This is joint work with Ali Enayat, myself and Bartosz Wcisło.
- - - - Thursday, Nov 12, 2020 - - - -
- - - - Friday, Nov 13, 2020 - - - -
Diana Montoya, University of Vienna
Independence and uncountable cardinals
The classical concept of independence, first introduced by Fichtenholz and Kantorovic has been of interest within the study of combinatorics of the subsets of the real line. In particular the study of the cardinal characteristic i defined as the minimum size of a maximal independent family of subsets of ω. In the first part of the talk, we will review the basic theory, as well as the most important results regarding the independence number. We will also point out our construction of a poset P forcing a maximal independent family of minimal size which turns out to be indestructible after forcing with a countable support iteration of Sacks forcing.
In the second part, we will talk about the generalization (or possible generalizations) of the concept of independence in the generalized Baire spaces, i.e. within the space κκ when κ is a regular uncountable cardinal and the new challenges this generalization entails. Moreover, for a specific version of generalized independence, we can have an analogous result to the one mentioned in the paragraph above.
This is joint work with Vera Fischer.
- - - - Monday, Nov 16, 2020 - - - -
Logic and Metaphysics Workshop
Date: Monday, November 16, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu
- - - - Tuesday, Nov 17, 2020 - - - -
- - - - Wednesday, Nov 18, 2020 - - - -
- - - - Thursday, Nov 19, 2020 - - - -
- - - - Friday, Nov 20, 2020 - - - -
Philipp Schlicht University of Vienna
TBA
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Barcelona Set Theory Seminar
Seminar at 11 am (Friday 13th) and back to normal following week
11:00 am
Ralf Schindler (University of Münster, Germany)
Title: Martin's Maximum^++ implies the P_max axiom (*).
Abstract: Forcing axioms spell out the dictum that if a statement can be
forced, then it is already true. The P_max axiom (*) goes beyond that by
claiming that if a statement is consistent, then it is already true.
Here, the statement in question needs to come from a resticted class of
statements, and "consistent" needs to mean "consistent in a strong
sense." It turns out that (*) is actually equivalent to a forcing axiom,
and the proof is by showing that the (strong) consistency of certain
theories gives rise to a corresponding notion of forcing producing a
model of that theory. This is joint work with D. Asperó building upon
earlier work of R. Jensen and (ultimately) Keisler's "consistency
properties."
1:30 pm
Andrea Medini (University of Vienna, Austria)
Title: Topological applications of Wadge theory
Abstract: Wadge theory provides an exhaustive analysis of the
topological complexity of the subsets of a zero-dimensional Polish
space. Fons van Engelen pioneered its applications to topology by
obtaining a classification of the zero-dimensional homogeneous Borel
spaces (recall that a space $X$ is homogeneous if for all $x,y\in X$
there exists a homeomorphism $h:X\longrightarrow X$ such that $h(x)=y$).
As a corollary, he showed that all such spaces (apart from trivial
exceptions) are in fact strongly homogeneous (recall that a space $X$ is
strongly homogeneous if all non-empty clopen subspaces of $X$ are
homeomorphic to each other).
In a joint work with the other members of the “Wadge Brigade” (namely,
Raphaël Carroy and Sandra Müller), we showed that this last result
extends beyond the Borel realm if one assumes AD. We intend to sketch
the proof of this theorem, with a view towards a complete classification
of the zero-dimensional homogeneous spaces under AD.
Reminder: Toronto Set Theory Seminar Talk Today (in 15 minutes)
Title: Definable maximal families of reals in forcing extensions
Abstract: Many types of combinatorial, algebraic or measure-theoretic
families of reals, such as mad families, Hamel bases or Vitali sets, can
be framed as maximal independent sets in analytic hypergraphs on Polish
spaces. Their existence is guaranteed by the Axiom of Choice, but
low-projective witnesses ($\mathbf{Delta}^1_2$) were only known to exist
in general in models of the form $L[a]$ for a real $a$. Our main result
is that, after a countable support iteration of Sacks forcing or for
example splitting forcing (a less known forcing adding splitting reals)
over L, every analytic hypergraph on a Polish space has a
$\mathbf{\Delta}^1_2$ maximal independent set. As a corollary, this
solves an open problem of Brendle, Fischer and Khomskii by providing a
model with a $\Pi^1_1$ mif (maximal independent family) while the
Logic Seminar 11 Nov 2020 17:00 hrs at NUS by Philipp Schlicht
Matt Foreman: Hilbert's 10th problem for dynamical systems
(KGRC) research seminar talk on Thursday, November 5
Logic Seminar 4 Nov 2020 17:00 hrs at NUS by Andre Nies
This Week in Logic at CUNY
Logic and Metaphysics Workshop
Date: Monday, November 2, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu
Speaker: Heinrich Wansing (Bochum)
Title: A Note on Synonymy in Proof-Theoretic Semantics
Abstract: The topic of identity of proofs was put on the agenda of general (or structural) proof theory at an early stage. The relevant question is: When are the differences between two distinct proofs (understood as linguistic entities, proof figures) of one and the same formula so inessential that it is justified to identify the two proofs? The paper addresses another question: When are the differences between two distinct formulas so inessential that these formulas admit of identical proofs? The question appears to be especially natural if the idea of working with more than one kind of derivations is taken seriously. If a distinction is drawn between proofs and disproofs (or refutations) as primitive entities, it is quite conceivable that a proof of one formula amounts to a disproof of another formula, and vice versa. The paper develops this idea.
- - - - Tuesday, Nov 3, 2020 - - - -
Speaker: Sergei Artemov, Graduate Center CUNY
In this project, we pursue two principal ideas: (i) justifications are prime objects of epistemic modeling: knowledge and belief are defined evidence-based concepts; (ii) awareness restrictions are applied to justifications rather than to propositions, which allows for the maintaining of desirable closure properties. The basic resulting structures, Justification Awareness Models, JAMs, naturally include major justification models, Kripke models and, in addition, represent situations with multiple possibly fallible justifications which, in full generality, were previously off the scope of rigorous epistemic modeling.
- - - - Wednesday, Nov 4, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, Oct 28, 3:00pm
The seminar will take place virtually at 3pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Victoria Gitman, CUNY
A model of second-order arithmetic satisfying AC but not DC: Part II
One of the strongest second-order arithmetic systems is full second-order arithmetic Z2 which asserts that every second-order formula (with any number of set quantifiers) defines a set. We can augment Z2 with choice principles such as the choice scheme and the dependent choice scheme. The Σ1n-choice scheme asserts for every Σ1n-formula φ(n,X) that if for every n, there is a set X witnessing φ(n,X), then there is a single set Z whose n-th slice Zn is a witness for φ(n,X). The Σ1n-dependent choice scheme asserts that every Σ1n-relation φ(X,Y) without terminal nodes has an infinite branch: there is a set Z such that φ(Zn,Zn+1) holds for all n. The system Z2 proves the Σ12-choice scheme and the Σ12-dependent choice scheme. The independence of Π12-choice scheme from Z2 follows by taking a model of Z2 whose sets are the reals of the Feferman-Levy model of ZF in which every ℵLn is countable and ℵLω is the first uncountable cardinal.
We construct a model of ZF+ACω whose reals give a model of Z2 together with the full choice scheme in which Π12-dependent choice fails. This result was first proved by Kanovei in 1979 and published in Russian. It was rediscovered by Sy Friedman and myself with a slightly simplified proof.
- - - - Thursday, Nov 5, 2020 - - - -
On Thursday, November 5 (6:30 PM) we will return to the book by Diaconis and Skyrms . The Zoom talk will be led by Paul Pedersen.
Title: Inverse Inference from Bayes and Laplace to Statistics.
Abstract: You are screening new drugs for a certain disease. Some patients get better by at least a certain amount; some don't. For one new drug, more get better on the drug than on a placebo. How confident should you be of the new drug's effectiveness on the evidence?
A Zoom link will be posted on the webpage https://philog.arthurpaulpedersen.org/
- - - - Friday, Nov 6, 2020 - - - -
Covering at limit cardinals of K
Theorem (Mitchell and Schimmerling, submitted for publication) Assume there is no transitive class model of ZFC with a Woodin cardinal. Let ν be a singular ordinal such that ν>ω2 and cf(ν)<|ν|. Suppose ν is a regular cardinal in K. Then ν is a measurable cardinal in K. Moreover, if cf(ν)>ω, then oK(ν)≥cf(ν).
I will say something intuitive and wildly incomplete but not misleading about the meaning of the theorem, how it is proved, and the history of results behind it.
- - - - Monday, Nov 9, 2020 - - - -
Logic and Metaphysics Workshop
Date: Monday, November 9, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu
Eoin Moore (CUNY)
Title: Towards a Justification Logic for FDE
Abstract: In this work-in-progress, I aim to develop a justification logic counterpart to first degree entailment. I produce a logic which is an extension of FDE using justification terms. The results are extended to other paraconsistent logics.
- - - - Tuesday, Nov 10, 2020 - - - -
- - - - Wednesday, Nov 11, 2020 - - - -
- - - - Thursday, Nov 12, 2020 - - - -
- - - - Friday, Nov 13, 2020 - - - -
Diana Montoya, University of Vienna
TBA
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Seminar next week
Jonathan Schilhan (University of Vienna, Austria)
Title: Definable maximal families of reals in forcing extensions
Abstract: Many types of combinatorial, algebraic or measure-theoretic
families of reals, such as mad families, Hamel bases or Vitali sets, can
be framed as maximal independent sets in analytic hypergraphs on Polish
spaces. Their existence is guaranteed by the Axiom of Choice, but
low-projective witnesses ($\mathbf{Delta}^1_2$) were only known to exist
in general in models of the form $L[a]$ for a real $a$. Our main result
is that, after a countable support iteration of Sacks forcing or for
example splitting forcing (a less known forcing adding splitting reals)
over L, every analytic hypergraph on a Polish space has a
$\mathbf{\Delta}^1_2$ maximal independent set. As a corollary, this
solves an open problem of Brendle, Fischer and Khomskii by providing a
model with a $\Pi^1_1$ mif (maximal independent family) while the
independence number $\mathfrak{i}$ is bigger than $\aleph_1$.
-----
Nov 13th
11:00 am
Ralf Schindler (University of Münster, Germany)
Title: Martin's Maximum^++ implies the P_max axiom (*).
Abstract: Forcing axioms spell out the dictum that if a statement can be
forced, then it is already true. The P_max axiom (*) goes beyond that by
claiming that if a statement is consistent, then it is already true.
Here, the statement in question needs to come from a resticted class of
statements, and "consistent" needs to mean "consistent in a strong
sense." It turns out that (*) is actually equivalent to a forcing axiom,
and the proof is by showing that the (strong) consistency of certain
theories gives rise to a corresponding notion of forcing producing a
model of that theory. This is joint work with D. Asperó building upon
earlier work of R. Jensen and (ultimately) Keisler's "consistency
properties."
------
Nov 20th
1:30 pm
Andrea Medini (University of Vienna, Austria)
Title: Topological applications of Wadge theory
Abstract: Wadge theory provides an exhaustive analysis of the
topological complexity of the subsets of a zero-dimensional Polish
space. Fons van Engelen pioneered its applications to topology by
obtaining a classification of the zero-dimensional homogeneous Borel
spaces (recall that a space $X$ is homogeneous if for all $x,y\in X$
there exists a homeomorphism $h:X\longrightarrow X$ such that $h(x)=y$).
As a corollary, he showed that all such spaces (apart from trivial
exceptions) are in fact strongly homogeneous (recall that a space $X$ is
strongly homogeneous if all non-empty clopen subspaces of $X$ are
homeomorphic to each other).
In a joint work with the other members of the “Wadge Brigade” (namely,
Raphaël Carroy and Sandra Müller), we showed that this last result
extends beyond the Borel realm if one assumes AD. We intend to sketch
the proof of this theorem, with a view towards a complete classification
of the zero-dimensional homogeneous spaces under AD.
-----
Nov 27th
1:30 pm
Sandra Müller (University of Vienna, Austria)
Title: TBA
Seminar Today reminder (in half an hour)
Join Zoom Meeting
https://us02web.zoom.us/j/89076919828?pwd=Qy8zMGNvNzFrd0toSXQxTThxVkZVUT09
Meeting ID: 890 7691 9828
Passcode: 670870
Barcelona Set Theory Seminar
(KGRC) research seminar talk on Thursday, October 29
Toronto Set Theory Seminar (First talk of this Term)
Join Zoom Meeting
https://us02web.zoom.us/j/89076919828?pwd=Qy8zMGNvNzFrd0toSXQxTThxVkZVUT09
Meeting ID: 890 7691 9828
Passcode: 670870
This Week in Logic at CUNY
Logic and Metaphysics Workshop
Date: Monday, October 26th, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu
Speaker: Lisa Warenski (CUNY)
Title: The Metaphysics of Epistemic Norms
Abstract: A metanormative theory inter alia gives an account of the objectivity of normative claims and addresses the ontological status of normative properties in its target domain. A metanormative theory will thus provide a framework for interpreting the claims of its target first-order theory. Some irrealist metanormative theories (e.g., Gibbard 1990 and Field 2000, 2009) conceive of normative properties as evaluative properties that may attributed to suitable objects of assessment (doxastic states, agents, or actions) in virtue of systems of norms. But what are the conditions for the acceptability of systems of norms, and relatedly, correctness of normative judgment? In this paper, I take up these questions for epistemic norms. Conditions for the acceptability of epistemic norms, and hence correctness of epistemic judgment, will be based on the critical evaluation of norms for their ability to realize our epistemic aims and values. Epistemic aims and values, in turn, are understood to be generated from the epistemic point of view, namely the standpoint of valuing truth.
- - - - Tuesday, Oct 27, 2020 - - - -
- - - - Wednesday, Oct 28, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, Oct 28, 3:00pm
The seminar will take place virtually at 3pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Victoria Gitman, CUNY
A model of second-order arithmetic satisfying AC but not DC
One of the strongest second-order arithmetic systems is full second-order arithmetic Z2 which asserts that every second-order formula (with any number of set quantifiers) defines a set. We can augment Z2 with choice principles such as the choice scheme and the dependent choice scheme. The Σ1n-choice scheme asserts for every Σ1n-formula φ(n,X) that if for every n, there is a set X witnessing φ(n,X), then there is a single set Z whose n-th slice Zn is a witness for φ(n,X). The Σ1n-dependent choice scheme asserts that every Σ1n-relation φ(X,Y) without terminal nodes has an infinite branch: there is a set Z such that φ(Zn,Zn+1) holds for all n. The system Z2 proves the Σ12-choice scheme and the Σ12-dependent choice scheme. The independence of Π12-choice scheme from Z2 follows by taking a model of Z2 whose sets are the reals of the Feferman-Levy model of ZF in which every ℵLn is countable and ℵLω is the first uncountable cardinal.
We construct a model of ZF+ACω whose reals give a model of Z2 together with the full choice scheme in which Π12-dependent choice fails. This result was first proved by Kanovei in 1979 and published in Russian. It was rediscovered by Sy Friedman and myself with a slightly simplified proof.
- - - - Thursday, Oct 29, 2020 - - - -
Zoom seminar, Thursday October 29 at 6:30 PM
Cailin O'Connor, UC Irvine
A zoom link will be posted on Wednesday at
https://philog.arthurpaulpedersen.org/
- - - - Friday, Oct 30, 2020 - - - -
TBA
Workshop on Substructural Logics, Hierarchies Thereof, and Solutions to the Liar
10.00. Strict/Tolerant and Tolerant/Strict Logics, Melvin Fitting, CUNY.
11.40. Expressibility and the (Un)paradoxicality Paradoxes, Will Nava, NYU.
1.20. Lunch Break.
2.00. What is Meta-inferential Validity?, Chris Scambler, NYU.
3.40. Supervaluations and the Strict-Tolerant Hierarchy, Brian Porter, CUNY.
5.20. End (virtual gathering).
Talks will be on Zoom, and are open to all interested. A link will be sent out on the mailing lists of the Logic and Metaphysics Workshop and the Saul Kripke Center the day before. People not on either of those lists who want to receive the link should email Graham Priest (priest DOT graham AT gmail DOT com). PLEASE FEEL FREE TO PASS ON THIS ANNOUNCEMENT.
- - - - Monday, Nov 2, 2020 - - - -
Logic and Metaphysics Workshop
Date: Monday, November 2, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu
Speaker: Lisa Warenski (CUNY).
Title: The Metaphysics of Epistemic Norms
Abstract: A metanormative theory inter alia gives an account of the objectivity of normative claims and addresses the ontological status of normative properties in its target domain. A metanormative theory will thus provide a framework for interpreting the claims of its target first-order theory. Some irrealist metanormative theories (e.g., Gibbard 1990 and Field 2000, 2009) conceive of normative properties as evaluative properties that may attributed to suitable objects of assessment (doxastic states, agents, or actions) in virtue of systems of norms. But what are the conditions for the acceptability of systems of norms, and relatedly, correctness of normative judgment? In this paper, I take up these questions for epistemic norms. Conditions for the acceptability of epistemic norms, and hence correctness of epistemic judgment, will be based on the critical evaluation of norms for their ability to realize our epistemic aims and values. Epistemic aims and values, in turn, are understood to be generated from the epistemic point of view, namely the standpoint of valuing truth.
- - - - Tuesday, Nov 3, 2020 - - - -
- - - - Wednesday, Nov 4, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, Oct 28, 3:00pm
The seminar will take place virtually at 3pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Victoria Gitman, CUNY
A model of second-order arithmetic satisfying AC but not DC: Part II
One of the strongest second-order arithmetic systems is full second-order arithmetic Z2 which asserts that every second-order formula (with any number of set quantifiers) defines a set. We can augment Z2 with choice principles such as the choice scheme and the dependent choice scheme. The Σ1n-choice scheme asserts for every Σ1n-formula φ(n,X) that if for every n, there is a set X witnessing φ(n,X), then there is a single set Z whose n-th slice Zn is a witness for φ(n,X). The Σ1n-dependent choice scheme asserts that every Σ1n-relation φ(X,Y) without terminal nodes has an infinite branch: there is a set Z such that φ(Zn,Zn+1) holds for all n. The system Z2 proves the Σ12-choice scheme and the Σ12-dependent choice scheme. The independence of Π12-choice scheme from Z2 follows by taking a model of Z2 whose sets are the reals of the Feferman-Levy model of ZF in which every ℵLn is countable and ℵLω is the first uncountable cardinal.
We construct a model of ZF+ACω whose reals give a model of Z2 together with the full choice scheme in which Π12-dependent choice fails. This result was first proved by Kanovei in 1979 and published in Russian. It was rediscovered by Sy Friedman and myself with a slightly simplified proof.
- - - - Thursday, Nov 5, 2020 - - - -
- - - - Friday, Nov 6, 2020 - - - -
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Barcelona Set Theory Seminar
(KGRC) research seminar talk on Thursday, October 22
Barcelona Set Theory Seminar
Barcelona Set Theory Seminar
This Week in Logic at CUNY
- - - - Monday, Oct 19, 2020 - - - -
Logic and Metaphysics Workshop
Date: Monday, October 19th, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu
Abstract: In this paper, I shall return to the relations between logic and semantics of natural language. My main goal is to advance a proposal about what that relation is. Logic as used in the study of natural language—an empirical discipline—functions much like specific kinds of scientific models. Particularly, I shall suggest, logics can function like analogical models. More provocatively, I shall also suggest they can function like model organisms often do in the biological sciences, providing a kind of controlled environment for observations. My focus here will be on a wide family of logics that are based on model theory, so in the end, these claims apply equally to model theory itself. Along the way towards arguing for my thesis about models in science, I shall also try to clarify the role of model theory in logic. At least, I shall suggest, it can play distinct roles in each domain. It can offer something like scientific models when it comes to empirical applications, while at the same time furthering conceptual analysis of a basic notion of logic.
- - - - Tuesday, Oct 20, 2020 - - - -
Abstract: We say that an agent desires a condition phi if (1) the agent knows neither that phi is true nor that phi is false (2) among all indistinguishable worlds, she prefers those in which phi is true. In this talk, I will propose a sound and complete logical system that describes the interplay between the desire and the knowledge modalities in the multiagent setting.
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, Oct 21, 7:00pm
The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Types, gaps, and pairs of models of PA, Part III
Speaker: Andrei V. Rodin, Saint Petersburg State University.
Date and Time: Wednesday October 21, 2020, 7:00 - 8:30 PM., on Zoom.
TBA
- - - - Thursday, Oct 22, 2020 - - - -
- - - - Friday, Oct 23, 2020 - - - -
Ultrapowers and the approximation property
Countably complete ultrafilters are the combinatorial manifestation of strong large cardinal axioms, but many of their basic properties are undecidable no matter the large cardinal axioms one is willing to adopt. The Ultrapower Axiom (UA) is a set theoretic principle that permits the development of a much clearer picture of countably complete ultrafilters and, consequently, the large cardinals from which they derive. It is not known whether UA is (relatively) consistent with very large cardinals, but assuming there is a canonical inner model with a supercompact cardinal, the answer should be yes: this inner model should satisfy UA and yet inherit all large cardinals present in the universe of sets. The predicted resemblance between the large cardinal structure of this model and that of the universe itself is so extreme as to suggest that certain consequences of UA must in fact be provable outright from large cardinal axioms. While the inner model theory of supercompact cardinals remains a major open problem, this talk will describe a technique that already permits a number of consequences of UA to be replicated from large cardinals alone. Still, the technique rests on the existence of inner models that absorb large cardinals, but instead of building canonical inner models, one takes ultrapowers.
- - - - Monday, Oct 26, 2020 - - - -
- - - - Tuesday, Oct 27, 2020 - - - -
- - - - Wednesday, Oct 28, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, Oct 28, 2:00pm
The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Victoria Gitman, CUNY
A model of second-order arithmetic satisfying AC but not DC
One of the strongest second-order arithmetic systems is full second-order arithmetic Z2 which asserts that every second-order formula (with any number of set quantifiers) defines a set. We can augment Z2 with choice principles such as the choice scheme and the dependent choice scheme. The Σ1n-choice scheme asserts for every Σ1n-formula φ(n,X) that if for every n, there is a set X witnessing φ(n,X), then there is a single set Z whose n-th slice Zn is a witness for φ(n,X). The Σ1n-dependent choice scheme asserts that every Σ1n-relation φ(X,Y) without terminal nodes has an infinite branch: there is a set Z such that φ(Zn,Zn+1) holds for all n. The system Z2 proves the Σ12-choice scheme and the Σ12-dependent choice scheme. The independence of Π12-choice scheme from Z2 follows by taking a model of Z2 whose sets are the reals of the Feferman-Levy model of ZF in which every ℵLn is countable and ℵLω is the first uncountable cardinal.
We construct a model of ZF+ACω whose reals give a model of Z2 together with the full choice scheme in which Π12-dependent choice fails. This result was first proved by Kanovei in 1979 and published in Russian. It was rediscovered by Sy Friedman and myself with a slightly simplified proof.
- - - - Thursday, Oct 29, 2020 - - - -
- - - - Friday, Oct 30, 2020 - - - -
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Logic Seminar 21 Oct 2020 17:00 hrs at NUS by Rupert Hoelzl (Universitaet der Bundeswehr Muenchen)
Logic Seminar 28 Oct 2020 17:00 hrs at NUS by Liao Luke
Logic Seminar 28 Oct 2020 17:00 hrs at NUS by Liao Yuke (typing errors corrected)
(KGRC) research seminar talk on Thursday, October 15
This Week in Logic at CUNY
- - - - Monday, Oct 12, 2020 - - - -
Logic and Metaphysics Workshop
Date: Monday, October 12th, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu
Brian Cross Porter (CUNY).
Title: A Metainferential Hierachy of Validity Curry Paradoxes
Abstract: The validity curry paradox is a paradox involving a validity predicate which does not use any of the logical connectives; triviality can be derived using only the structural rules of Cut and Contraction with intuitively plausible rules for the validity predicate. This has been used to argue that we should move to a substructural logic dropping Cut or Contraction. In this talk, I’ll present metainferential versions of the validity curry paradox. We can recreate the validity curry paradox at the metainferential level, the metametainferential level, the metametametainferential level, and so on ad infinitum. I argue that this hierarchy of metaninferential validity curry paradoxes poses a problem for the standard substructural solutions to the validity curry paradox.
- - - - Tuesday, Oct 13, 2020 - - - -
- - - - Wednesday, Oct 14, 2020 - - - -
Date and Time: Wednesday October 14, 2020, 6:00 - 7:30PM (NOTICE DIFFERENT TIME) on Zoom.
Title: Pseudogroup Torsors.
Abstract: We use sheaf theory to analyze the topos of etale actions on the germ groupoid of a pseudogroup in the sense that we present a site for this topos, which we call the classifying topos of the pseudogroup. Our analysis carries us further into how pseudogroup morphisms and geometric morphisms are related. Ultimately, we shall see that the classifying topos classifies what we call a pseudogroup torsor. In hindsight, we see that pseudogroups form a bicategory of `flat' bimodules.
Joint work with Pieter Hofstra.
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, Oct 14, 7:00pm
The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Types, gaps, and pairs of models of PA, Part II
- - - - Thursday, Oct 15, 2020 - - - -
- - - - Friday, Oct 16, 2020 - - - -
Taking Reinhardt's Power Away
Many large cardinals can be defined through elementary embeddings from the set-theoretic universe to some inner model, with the guiding principle being that the closer the inner model is to the universe the stronger the resulting theory. Under ZFC, the Kunen Inconsistency places a hard limit on how close this can be. One is then naturally led to the question of what theory is necessary to derive this inconsistency with the primary focus having historically been embeddings in ZF without Choice.
In this talk we take a different approach to weakening the required theory, which is to study elementary embeddings from the universe into itself in ZFC without Power Set. We shall see that I1, one of the largest large cardinal axioms not known to be inconsistent with ZFC, gives an upper bound to the naive version of this question. However, under reasonable assumptions, we can reobtain this inconsistency in our weaker theory.
- - - - Monday, Oct 19, 2020 - - - -
Logic and Metaphysics Workshop
Date: Monday, October 19th, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu
Abstract: In this paper, I shall return to the relations between logic and semantics of natural language. My main goal is to advance a proposal about what that relation is. Logic as used in the study of natural language—an empirical discipline—functions much like specific kinds of scientific models. Particularly, I shall suggest, logics can function like analogical models. More provocatively, I shall also suggest they can function like model organisms often do in the biological sciences, providing a kind of controlled environment for observations. My focus here will be on a wide family of logics that are based on model theory, so in the end, these claims apply equally to model theory itself. Along the way towards arguing for my thesis about models in science, I shall also try to clarify the role of model theory in logic. At least, I shall suggest, it can play distinct roles in each domain. It can offer something like scientific models when it comes to empirical applications, while at the same time furthering conceptual analysis of a basic notion of logic.
- - - - Tuesday, Oct 20, 2020 - - - -
- - - - Wednesday, Oct 21, 2020 - - - -
The New York City Category Theory Seminar
Speaker: Andrei V. Rodin, Saint Petersburg State University.
Date and Time: Wednesday October 21, 2020, 7:00 - 8:30 PM., on Zoom.
TBA
- - - - Thursday, Oct 22, 2020 - - - -
- - - - Friday, Oct 23, 2020 - - - -
TBA
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Wednesday seminar
Barcelona Set Theory Seminar
Logic Seminar 14 Oct 2020 17:00 hrs at NUS by Tran Chieu-Minh (University of Notre Dame)
Link to the Barcelona Set Theory Seminar
Clovis Hamel: An introduction to Cp-theory and Grothendieck spaces
(KGRC) research seminar talk on Thursday, October 8
This Week in Logic at CUNY
- - - - Monday, Oct 5, 2020 - - - -
Logic and Metaphysics Workshop
Date: Monday, October 5th, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu
Speaker: Oliver Marshall (UNAM)
Title: Mathematical Information Content
Abstract: Alonzo Church formulated several logistic theories of propositions based on three alternative criteria of identity (1949, 1954, 1989, 1993). The most coarse grained of these criteria is Alternative (2), according to which two propositions are identical iff the sentences that express them are necessarily materially equivalent. Alternative (1) is more discerning. According to Alternative (1), two propositions are identical iff the sentences that express them can be obtained from one another by the substitution of synonyms for synonyms and λ-conversion. Church said that he intended this to limn a notion of proposition closely related to Frege’s notion of gedanke, but added that it will not be sufficiently discerning if propositions in the sense of Alternative (1) are taken as objects of assertion and belief (1993). Alternative (0), the most discerning criterion, says that two propositions are identical iff the sentences that express them can be obtained from one another by the substitution of synonyms for synonyms. I argue that Alternative (1) does indeed provide insight into one of the topics that concerned Frege (1884) – namely, abstraction. Then I discuss various counterexamples to Church’s criteria (including one due to Paul Bernays, 1961). I close by proposing a criterion of identity for mathematical information content based on the various examples under discussion.
- - - - Tuesday, Oct 6, 2020 - - - -
Title: Justification Logics as Internal Languages -- Part 1 of 2
This is the first of two talks in which I answer the question (in the affirmative) of whether the justification logic J is the internal language of a class of categories. In this first talk we will discuss the methods by which a logic may be interpreted in a category, and the properties such interpretations may have. Concrete examples will include propositional intuitionistic logic as the internal language of bi-Cartesian closed categories. Some aspects of the interpretation of higher logics in topoi will also be discussed. Previous knowledge of category theory is not assumed.
The talk concludes with a discussion of the difficulties inherent in the interpretation of justification logics. In the next talk, a class of categories is presented with respect to which the justification logic J is sound and complete in a weak sense.
- - - - Wednesday, Oct 7, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, Oct 7, 7:00pm
The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Types, gaps, and pairs of models of PA
- - - - Thursday, Oct 8, 2020 - - - -
- - - - Friday, Oct 9, 2020 - - - -
Heike Mildenberger, Albert-Ludwigs-Universität Freiburg
Forcing with variants of Miller trees
Guzmán and Kalajdzievski introduced a variant of Miller forcing P(F) that diagonalises a given filter F over ω and has Axiom A. We investigate the effect of P(F) for particularly chosen Canjar filters F. This is joint work with Christian Bräuninger.
- - - - Monday, Oct 12, 2020 - - - -
Logic and Metaphysics Workshop
Date: Monday, October 12th, 4.15-6.15 (NY time)
For meeting information, please email: yweiss@gradcenter.cuny.edu
Brian Cross Porter (CUNY).
Title: A Metainferential Hierachy of Validity Curry Paradoxes
Abstract: The validity curry paradox is a paradox involving a validity predicate which does not use any of the logical connectives; triviality can be derived using only the structural rules of Cut and Contraction with intuitively plausible rules for the validity predicate. This has been used to argue that we should move to a substructural logic dropping Cut or Contraction. In this talk, I’ll present metainferential versions of the validity curry paradox. We can recreate the validity curry paradox at the metainferential level, the metametainferential level, the metametametainferential level, and so on ad infinitum. I argue that this hierarchy of metaninferential validity curry paradoxes poses a problem for the standard substructural solutions to the validity curry paradox.
- - - - Tuesday, Oct 13, 2020 - - - -
- - - - Wednesday, Oct 14, 2020 - - - -
Date and Time: Wednesday October 14, 2020, 6:00 - 7:30PM (NOTICE DIFFERENT TIME) on Zoom.
Title: Pseudogroup Torsors.
Abstract: We use sheaf theory to analyze the topos of etale actions on the germ groupoid of a pseudogroup in the sense that we present a site for this topos, which we call the classifying topos of the pseudogroup. Our analysis carries us further into how pseudogroup morphisms and geometric morphisms are related. Ultimately, we shall see that the classifying topos classifies what we call a pseudogroup torsor. In hindsight, we see that pseudogroups form a bicategory of `flat' bimodules.
Joint work with Pieter Hofstra.
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, Oct 14, 7:00pm
The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Types, gaps, and pairs of models of PA
- - - - Thursday, Oct 15, 2020 - - - -
- - - - Friday, Oct 16, 2020 - - - -
TBA
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Wednesday seminar
Invitation to Logic Seminar 7 Oct 2020 17:00 hrs at NUS by Wu Guohua
Barcelona Set Theory seminar
This Week in Logic at CUNY
Logic and Metaphysics Workshop
Date: Monday, September 21st, 4.15-6.15 (NY time)
Speaker: Yale Weiss (CUNY)
Title: Arithmetical Semantics for Non-Classical Logic
Abstract: I consider logics which can be characterized exactly in the lattice of the positive integers ordered by division. I show that various (fragments of) relevant logics and intuitionistic logic are sound and complete with respect to this structure taken as a frame; different logics are characterized in it by imposing different conditions on valuations. This presentation will both cover and extend previous/forthcoming work of mine on the subject.
- - - - Tuesday, Sep 22, 2020 - - - -
Computational Logic Seminar
Time 2:00 - 4:00 PM Tuesday, September 22, 2020
Please send me a request for a link to this talk: (unless you are registered or have already sent me a request for the whole semester).
Speaker: Hirohiko Kushida, Graduate Center, City University of New York
Title: Reduction of Modal Logic and Realization in Justification Logic
- - - - Wednesday, Sep 23, 2020 - - - -
- - - - Thursday, Sep 24, 2020 - - - -
Seminar in Philosophical Logic
Thursday, Sep 24, 6:30 PM.
(Zoom link upon request RParikh@gc.cuny.edu; will be sent automatically to seminar members)
Arthur Paul Pedersen, Department of Computer Science, City College of New York, CUNY
Coherent Judgment: Previsions and Forecasts
- - - - Friday, Sep 25, 2020 - - - -
Forcing axioms spell out the dictum that if a statement can be forced, then it is already true. The P_max axiom (*) goes beyond that by claiming that if a statement is consistent, then it is already true. Here, the statement in question needs to come from a resticted class of statements, and 'consistent' needs to mean 'consistent in a strong sense.' It turns out that (*) is actually equivalent to a forcing axiom, and the proof is by showing that the (strong) consistency of certain theories gives rise to a corresponding notion of forcing producing a model of that theory. This is joint work with D. Asperó building upon earlier work of R. Jensen and (ultimately) Keisler's 'consistency properties'.
- - - - Monday, Sep 28, 2020 - - - -
Date: Monday, September 29st, 4.15-6.15 (NY time)
Speaker: Daniel Hoek (Virginia Tech)
Title: Coin flips, Spinning Tops and the Continuum Hypothesis
Abstract: By using a roulette wheel or by flipping a countable infinity of fair coins, we can randomly pick out a point on a continuum. In this talk I will show how to combine this simple observation with general facts about chance to investigate the cardinality of the continuum. In particular I will argue on this basis that the continuum hypothesis is false. More specifically, I argue that the probabilistic inductive methods standardly used in science presuppose that every proposition about the outcome of a chancy process has a certain chance between 0 and 1. I also argue in favour of the standard view that chances are countably additive. A classic theorem from Banach and Kuratowski (1929), tells us that it follows, given the axioms of ZFC, that there are cardinalities between countable infinity and the cardinality of the continuum. (Get the paper here: https://philpapers.org/archive/HOECAT-2.pdf).
- - - - Tuesday, Sep 29, 2020 - - - -
- - - - Wednesday, Sep 30, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, Sep 30, 2:00pm
The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Leszek Kołodziejczyk University of Warsaw
Ramsey's Theorem over RCA∗0: Part II
Abstract: The usual base theory used in reverse mathematics, RCA0, is the fragment of second-order arithmetic axiomatized by Δ01 comprehension and Σ01 induction. The weaker base theory RCA∗0 is obtained by replacing Σ01 induction with Δ01 induction (and adding the well-known axiom exp in order to ensure totality of the exponential function). In first-order terms, RCA0 is conservative over IΣ1 and RCA∗0 is conservative over BΣ1+exp.
Some of the most interesting open problems in reverse mathematics concern the first-order strength of statements from Ramsey Theory, in particular Ramsey's Theorem for pairs and two colours. In this talk, I will discuss joint work with Kasia Kowalik, Tin Lok Wong, and Keita Yokoyama concerning the strength of Ramsey's Theorem over RCA∗0.
Given standard natural numbers n,k≥2, let RTnk stand for Ramsey's Theorem for k-colourings of n-tuples. We first show that assuming the failure of Σ01 induction, RTnk is equivalent to its own relativization to an arbitrary Σ01-definable cut. Using this, we give a complete axiomatization of the first-order consequences of RCA∗0+RTnk for n≥3 (this turns out to be a rather peculiar fragment of PA) and obtain some nontrivial information about the first-order consequences of RT2k. Time permitting, we will also discuss the question whether our results have any relevance for the well-known open problem of characterizing the first-order consequences of RT22 over the traditional base theory RCA0.In the first part of the talk, we concentrated on Ramsey's Theorem for n-tuples where n≥3. In this second part, the focus will be on RT22.
The New York City Category Theory Seminar
Date and Time: Wednesday September 30, 2020, 7:00 - 8:30 PM., on Zoom.
Zoom information will be posted on the web page on the day of the talk http://www.sci.brooklyn.cuny.edu/~noson/CTseminar.html
Title: The Logical Theory of Canonical Maps: The Elements & Distinctions Analysis of the Morphisms, Duality, Canonicity, and Universal Constructions in Sets.
Abstract: Category theory gives a mathematical characterization of naturality but not of canonicity. The purpose of this paper is to develop the logical theory of canonical maps based on the broader demonstration that the dual notions of elements & distinctions are the basic analytical concepts needed to unpack and analyze morphisms, duality, canonicity, and universal constructions in Sets, the category of sets and functions. The analysis extends directly to other Sets-based concrete categories (groups, rings, vector spaces, etc.). Elements and distinctions are the building blocks of the two dual logics, the Boolean logic of subsets and the logic of partitions. The partial orders (inclusion and refinement) in the lattices for the dual logics define morphisms. The thesis is that the maps that are canonical in Sets are the ones that are defined (given the data of the situation) by these two logical partial orders and by the compositions of those maps.
Paper: Available here http://www.sci.brooklyn.cuny.edu/~noson/Ellerman2020.pdf
- - - - Friday, Oct 2, 2020 - - - -
- - - - Monday, Oct 5, 2020 - - - -
- - - - Tuesday, Oct 6, 2020 - - - -
- - - - Wednesday, Oct 7, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, Oct 7, 7:00pm
The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Types, gaps, and pairs of models of PA
- - - - Thursday, Oct 8, 2020 - - - -
- - - - Friday, Oct 9, 2020 - - - -
TBA
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Wednesday seminar
Logic Seminar 30 Sept 2020 17:00 hrs by Vasco Brattka (Universitaet der Bundeswehr Muenchen)
UPDATE - This Week in Logic at CUNY
Logic and Metaphysics Workshop
Date: Monday, September 21st, 4.15-6.15 (NY time)
Speaker: Yale Weiss (CUNY)
Title: Arithmetical Semantics for Non-Classical Logic
Abstract: I consider logics which can be characterized exactly in the lattice of the positive integers ordered by division. I show that various (fragments of) relevant logics and intuitionistic logic are sound and complete with respect to this structure taken as a frame; different logics are characterized in it by imposing different conditions on valuations. This presentation will both cover and extend previous/forthcoming work of mine on the subject.
- - - - Tuesday, Sep 22, 2020 - - - -
Computational Logic Seminar
Time 2:00 - 4:00 PM Tuesday, September 22, 2020
Please send me a request for a link to this talk: (unless you are registered or have already sent me a request for the whole semester).
Speaker: Hirohiko Kushida, Graduate Center, City University of New York
Title: Reduction of Modal Logic and Realization in Justification Logic
- - - - Wednesday, Sep 23, 2020 - - - -
- - - - Thursday, Sep 24, 2020 - - - -
Seminar in Philosophical Logic
Thursday, Sep 24, 6:30 PM.
(Zoom link upon request RParikh@gc.cuny.edu; will be sent automatically to seminar members)
Arthur Paul Pedersen, Department of Computer Science, City College of New York, CUNY
Coherent Judgment: Previsions and Forecasts
- - - - Friday, Sep 25, 2020 - - - -
Forcing axioms spell out the dictum that if a statement can be forced, then it is already true. The P_max axiom (*) goes beyond that by claiming that if a statement is consistent, then it is already true. Here, the statement in question needs to come from a resticted class of statements, and 'consistent' needs to mean 'consistent in a strong sense.' It turns out that (*) is actually equivalent to a forcing axiom, and the proof is by showing that the (strong) consistency of certain theories gives rise to a corresponding notion of forcing producing a model of that theory. This is joint work with D. Asperó building upon earlier work of R. Jensen and (ultimately) Keisler's 'consistency properties'.
- - - - Monday, Sep 28, 2020 - - - -
Date: Monday, September 29st, 4.15-6.15 (NY time)
Speaker: Daniel Hoek (Virginia Tech)
Title: Coin flips, Spinning Tops and the Continuum Hypothesis
Abstract: By using a roulette wheel or by flipping a countable infinity of fair coins, we can randomly pick out a point on a continuum. In this talk I will show how to combine this simple observation with general facts about chance to investigate the cardinality of the continuum. In particular I will argue on this basis that the continuum hypothesis is false. More specifically, I argue that the probabilistic inductive methods standardly used in science presuppose that every proposition about the outcome of a chancy process has a certain chance between 0 and 1. I also argue in favour of the standard view that chances are countably additive. A classic theorem from Banach and Kuratowski (1929), tells us that it follows, given the axioms of ZFC, that there are cardinalities between countable infinity and the cardinality of the continuum. (Get the paper here: https://philpapers.org/archive/HOECAT-2.pdf).
- - - - Tuesday, Sep 29, 2020 - - - -
- - - - Wednesday, Sep 30, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, Sep 30, 2:00pm
The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Leszek Kołodziejczyk University of Warsaw
Ramsey's Theorem over RCA∗0: Part II
Abstract: The usual base theory used in reverse mathematics, RCA0, is the fragment of second-order arithmetic axiomatized by Δ01 comprehension and Σ01 induction. The weaker base theory RCA∗0 is obtained by replacing Σ01 induction with Δ01 induction (and adding the well-known axiom exp in order to ensure totality of the exponential function). In first-order terms, RCA0 is conservative over IΣ1 and RCA∗0 is conservative over BΣ1+exp.
Some of the most interesting open problems in reverse mathematics concern the first-order strength of statements from Ramsey Theory, in particular Ramsey's Theorem for pairs and two colours. In this talk, I will discuss joint work with Kasia Kowalik, Tin Lok Wong, and Keita Yokoyama concerning the strength of Ramsey's Theorem over RCA∗0.
Given standard natural numbers n,k≥2, let RTnk stand for Ramsey's Theorem for k-colourings of n-tuples. We first show that assuming the failure of Σ01 induction, RTnk is equivalent to its own relativization to an arbitrary Σ01-definable cut. Using this, we give a complete axiomatization of the first-order consequences of RCA∗0+RTnk for n≥3 (this turns out to be a rather peculiar fragment of PA) and obtain some nontrivial information about the first-order consequences of RT2k. Time permitting, we will also discuss the question whether our results have any relevance for the well-known open problem of characterizing the first-order consequences of RT22 over the traditional base theory RCA0.In the first part of the talk, we concentrated on Ramsey's Theorem for n-tuples where n≥3. In this second part, the focus will be on RT22.
The New York City Category Theory Seminar
Date and Time: Wednesday September 30, 2020, 7:00 - 8:30 PM., on Zoom.
Zoom information will be posted on the web page on the day of the talk http://www.sci.brooklyn.cuny.edu/~noson/CTseminar.html
Title: The Logical Theory of Canonical Maps: The Elements & Distinctions Analysis of the Morphisms, Duality, Canonicity, and Universal Constructions in Sets.
Abstract: Category theory gives a mathematical characterization of naturality but not of canonicity. The purpose of this paper is to develop the logical theory of canonical maps based on the broader demonstration that the dual notions of elements & distinctions are the basic analytical concepts needed to unpack and analyze morphisms, duality, canonicity, and universal constructions in Sets, the category of sets and functions. The analysis extends directly to other Sets-based concrete categories (groups, rings, vector spaces, etc.). Elements and distinctions are the building blocks of the two dual logics, the Boolean logic of subsets and the logic of partitions. The partial orders (inclusion and refinement) in the lattices for the dual logics define morphisms. The thesis is that the maps that are canonical in Sets are the ones that are defined (given the data of the situation) by these two logical partial orders and by the compositions of those maps.
Paper: Available here http://www.sci.brooklyn.cuny.edu/~noson/Ellerman2020.pdf
- - - - Friday, Oct 2, 2020 - - - -
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
This Week in Logic at CUNY
Logic and Metaphysics Workshop
Date: Monday, September 21st, 4.15-6.15 (NY time)
Speaker: Yale Weiss (CUNY)
Title: Arithmetical Semantics for Non-Classical Logic
Abstract: I consider logics which can be characterized exactly in the lattice of the positive integers ordered by division. I show that various (fragments of) relevant logics and intuitionistic logic are sound and complete with respect to this structure taken as a frame; different logics are characterized in it by imposing different conditions on valuations. This presentation will both cover and extend previous/forthcoming work of mine on the subject.
- - - - Tuesday, Sep 22, 2020 - - - -
- - - - Wednesday, Sep 23, 2020 - - - -
- - - - Thursday, Sep 24, 2020 - - - -
Seminar in Philosophical Logic
Thursday, Sep 24, 6:30 PM.
(Zoom link upon request RParikh@gc.cuny.edu; will be sent automatically to seminar members)
Arthur Paul Pedersen, Department of Computer Science, City College of New York, CUNY
Coherent Judgment: Previsions and Forecasts
- - - - Friday, Sep 25, 2020 - - - -
Forcing axioms spell out the dictum that if a statement can be forced, then it is already true. The P_max axiom (*) goes beyond that by claiming that if a statement is consistent, then it is already true. Here, the statement in question needs to come from a resticted class of statements, and 'consistent' needs to mean 'consistent in a strong sense.' It turns out that (*) is actually equivalent to a forcing axiom, and the proof is by showing that the (strong) consistency of certain theories gives rise to a corresponding notion of forcing producing a model of that theory. This is joint work with D. Asperó building upon earlier work of R. Jensen and (ultimately) Keisler's 'consistency properties'.
- - - - Monday, Sep 28, 2020 - - - -
Date: Monday, September 29st, 4.15-6.15 (NY time)
Speaker: Daniel Hoek (Virginia Tech)
Title: Coin flips, Spinning Tops and the Continuum Hypothesis
Abstract: By using a roulette wheel or by flipping a countable infinity of fair coins, we can randomly pick out a point on a continuum. In this talk I will show how to combine this simple observation with general facts about chance to investigate the cardinality of the continuum. In particular I will argue on this basis that the continuum hypothesis is false. More specifically, I argue that the probabilistic inductive methods standardly used in science presuppose that every proposition about the outcome of a chancy process has a certain chance between 0 and 1. I also argue in favour of the standard view that chances are countably additive. A classic theorem from Banach and Kuratowski (1929), tells us that it follows, given the axioms of ZFC, that there are cardinalities between countable infinity and the cardinality of the continuum. (Get the paper here: https://philpapers.org/archive/HOECAT-2.pdf).
- - - - Tuesday, Sep 29, 2020 - - - -
- - - - Wednesday, Sep 30, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, Sep 30, 2:00pm
The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Leszek Kołodziejczyk University of Warsaw
Ramsey's Theorem over RCA∗0: Part II
Abstract: The usual base theory used in reverse mathematics, RCA0, is the fragment of second-order arithmetic axiomatized by Δ01 comprehension and Σ01 induction. The weaker base theory RCA∗0 is obtained by replacing Σ01 induction with Δ01 induction (and adding the well-known axiom exp in order to ensure totality of the exponential function). In first-order terms, RCA0 is conservative over IΣ1 and RCA∗0 is conservative over BΣ1+exp.
Some of the most interesting open problems in reverse mathematics concern the first-order strength of statements from Ramsey Theory, in particular Ramsey's Theorem for pairs and two colours. In this talk, I will discuss joint work with Kasia Kowalik, Tin Lok Wong, and Keita Yokoyama concerning the strength of Ramsey's Theorem over RCA∗0.
Given standard natural numbers n,k≥2, let RTnk stand for Ramsey's Theorem for k-colourings of n-tuples. We first show that assuming the failure of Σ01 induction, RTnk is equivalent to its own relativization to an arbitrary Σ01-definable cut. Using this, we give a complete axiomatization of the first-order consequences of RCA∗0+RTnk for n≥3 (this turns out to be a rather peculiar fragment of PA) and obtain some nontrivial information about the first-order consequences of RT2k. Time permitting, we will also discuss the question whether our results have any relevance for the well-known open problem of characterizing the first-order consequences of RT22 over the traditional base theory RCA0.In the first part of the talk, we concentrated on Ramsey's Theorem for n-tuples where n≥3. In this second part, the focus will be on RT22.
The New York City Category Theory Seminar
Date and Time: Wednesday September 30, 2020, 7:00 - 8:30 PM., on Zoom.
Zoom information will be posted on the web page on the day of the talk http://www.sci.brooklyn.cuny.edu/~noson/CTseminar.html
Title: The Logical Theory of Canonical Maps: The Elements & Distinctions Analysis of the Morphisms, Duality, Canonicity, and Universal Constructions in Sets.
Abstract: Category theory gives a mathematical characterization of naturality but not of canonicity. The purpose of this paper is to develop the logical theory of canonical maps based on the broader demonstration that the dual notions of elements & distinctions are the basic analytical concepts needed to unpack and analyze morphisms, duality, canonicity, and universal constructions in Sets, the category of sets and functions. The analysis extends directly to other Sets-based concrete categories (groups, rings, vector spaces, etc.). Elements and distinctions are the building blocks of the two dual logics, the Boolean logic of subsets and the logic of partitions. The partial orders (inclusion and refinement) in the lattices for the dual logics define morphisms. The thesis is that the maps that are canonical in Sets are the ones that are defined (given the data of the situation) by these two logical partial orders and by the compositions of those maps.
Paper: Available here http://www.sci.brooklyn.cuny.edu/~noson/Ellerman2020.pdf
- - - - Friday, Oct 2, 2020 - - - -
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Wednesday seminar
Roman Kossak: Truth, Resplendence, and Directed Graphs with Local Finite Height
Logic Seminar 16 Sept 2020 17:00 hrs at NUS by Ye Jinhe (Notre Dame)
This Week in Logic at CUNY
- - - - Monday, Sep 14, 2020 - - - -
Logic and Metaphysics Workshop
Date: Monday, September 14th, 4.15-6.15
For zoom information, email Yale Weiss at: yweiss@gradcenter.cuny.edu.
Speaker: Chris Scambler (NYU)
Title: Cantor’s Theorem, Modalized
Abstract: I will present a modal axiom system for set theory that (I claim) reconciles mathematics after Cantor with the idea there is only one size of infinity. I’ll begin with some philosophical background on Cantor’s proof and its relation to Russell’s paradox. I’ll then show how techniques developed to treat Russell’s paradox in modal set theory can be generalized to produce set theories consistent with the idea that there’s only one size of infinity.
- - - - Tuesday, Sep 15, 2020 - - - -
Fall 2020, on-line meetings
Please send me a request for a link to this talk - Sergei Artemov ()
Time 2:00 - 4:00 PM Tuesday
September 15, 2020
Speaker: Sergei Artemov, Graduate Center, City University of New York
Title: On Constructive Epistemic Logic
opened the door to a new avenue of active research in constructive epistemic logic. We will present the basics and comment on the current state of these studies.
- - - - Wednesday, Sep 16, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, Sep 16, 5:00pm
The seminar will take place virtually at 5pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Classification of countable models of ZFC
Date and Time: Wednesday September 16, 2020, 7:00 - 8:30 PM., on Zoom.
Zoom information will be posted on the web page on the day of the talk http://www.sci.brooklyn.cuny.edu/~noson/CTseminar.html
Expanding the domain of definition to extended pseudo metric spaces enables the construction of a realization functor on diagrams of spaces, which has a right adjoint Y |--> S(Y), called the singular functor. The realization of the Vietoris-Rips system V(X) for an ep-metric space X is the space itself. The counit of the adjunction defines a map \eta: V(X) --> S(X), which is a sectionwise weak equivalence - the proof uses simplicial approximation techniques.
This is the context for the Healy-McInnes UMAP construction, which will be discussed if time permits. UMAP is non-traditional: clusters for UMAP are defined by paths through sequences of neighbour pairs, which can be a highly efficient process in practice.
- - - - Thursday, Sep 17, 2020 - - - -
Zoom seminar in Philosophical Logic
Contact Rohit Parikh (rparikh@gc.cuny.edu) for zoom link.
Larry Moss of Indiana University will speak about Judgment from
- - - - Friday, Sep 18, 2020 - - - -
UA and the Number of Normal Measures over ℵω+1
The Ultrapower Axiom UA, introduced by Goldberg and Woodin, is known to have many striking consequences. In particular, Goldberg has shown that assuming UA, the Mitchell ordering of normal measures over a measurable cardinal is linear. I will discuss how this result may be used to construct choiceless models of ZF in which the number of normal measures at successors of singular cardinals can be precisely controlled.
- - - - Monday, Sep 21, 2020 - - - -
- - - - Tuesday, Sep 22, 2020 - - - -
- - - - Wednesday, Sep 23, 2020 - - - -
- - - - Thursday, Sep 24, 2020 - - - -
- - - - Friday, Sep 25, 2020 - - - -
Forcing axioms spell out the dictum that if a statement can be forced, then it is already true. The P_max axiom (*) goes beyond that by claiming that if a statement is consistent, then it is already true. Here, the statement in question needs to come from a resticted class of statements, and 'consistent' needs to mean 'consistent in a strong sense.' It turns out that (*) is actually equivalent to a forcing axiom, and the proof is by showing that the (strong) consistency of certain theories gives rise to a corresponding notion of forcing producing a model of that theory. This is joint work with D. Asperó building upon earlier work of R. Jensen and (ultimately) Keisler's 'consistency properties'.
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)
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Wednesday seminar
Wednesday seminar
Wednesday seminar
Kyoto University Research Institute for Mathematical Sciences Set Theory Workshop, November 16-20, 2020
This Week in Logic at CUNY
- - - - Monday, Sep 7, 2020 - - - -
- - - - Tuesday, Sep 8, 2020 - - - -
************************
Computational Logic Seminar
Fall 2020, on-line meetings
Time 2:00 - 4:00 PM Tuesday, September 8, 2020
Please send a request for a link to this talk (unless you are registered of have already sent me a request for the whole semester): sartemov@gc.cuny.edu
Speaker: Melvin Fitting, Graduate Center, City University of New York
Title: About `Binding Modalities'
In classical logic the addition of quantifiers to propositional logic is essentially unique, with some minor variations of course. In modal logic things are not so monolithic. One can quantify over things or over intensions; domains can be the same from possible world to possible world, or shrink, or grow, or follow no pattern, as one moves from a possible world to an accessible one. In 1963 Kripke showed that shrinking or growing domains related to validity of the Barcan and the converse Barcan formulas, but this was a semantic result. Proof theory is trickier. Nested sequents are well behaved, but axiom systems can be unruly. A direct combination of propositional modal axioms and rules with standard quantificational axioms and rules simply proves the converse Barcan formula. It's not easy to get rid of it. Kripke showed how one could do so, but he needed to use a less common axiomatization of the quantifiers. It works, but one has the impression of having a formal proof system with road blocks placed carefully to prevent proofs from veering into the ditch. Some 40 or more years later, justification logic was created by Artemov, and now there are justification systems that correspond to infinitely many different modal logics. The first justification logic was called LP, for logic of proofs. It is related to propositional S4. LP was extended to a quantified version by Artemov and Yavorskaya, with a possible world semantics supplied by Fitting. Subsequently Artemov and Yavorskaya transferred their ideas, concerning what they called binding modalities, back from quantified LP to quantified S4 itself. In the present work we carry their ideas on further to the basic normal modal logic, K, which is not as well-behaved as S4 on these matters. It turns out that this provides a natural intuition for Kripke's non-standard axiomatization from those many years ago. It also relates quite plausibly to the distinction between de re and de dicto. But now the main work is done through a generalization of the modal operator, instead of through a restriction on allowed quantifier axiomatizations.
- - - - Wednesday, Sep 9, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, Sep 9, 3:00pm
The seminar will take place virtually at 3pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Saeideh Bahrami, Institute for Research in Fundamental Sciences, TehranFixed Points of Initial Self-Embeddings of Models of Arithmetic
In 1973, Harvey Friedman proved his striking result on initial self-embeddings of countable nonstandard models of set theory and Peano arithmetic. In this talk, I will discuss my joint work with Ali Enayat focused on the fixed point set of initial self-embeddings of countable nonstandard models of arithmetic. Especially, I will survey the proof of some generalizations of well-known results on the fixed point set of automorphisms of countable recursively saturated models of PA, to results about the fixed point set of initial self-embeddings of countable nonstandard models of IΣ1.
- - - - Thursday, Sep 10, 2020 - - - -
- - - - Friday, Sep 11, 2020 - - - -
- - - - Monday, Sep 14, 2020 - - - -
Logic and Metaphysics Workshop
Date: Monday, September 14th, 4.15-6.15
For zoom information, email Yale Weiss at: yweiss@gradcenter.cuny.edu.
Speaker: Chris Scambler (NYU)
Title: Cantor’s Theorem, Modalized
Abstract: I will present a modal axiom system for set theory that (I claim) reconciles mathematics after Cantor with the idea there is only one size of infinity. I’ll begin with some philosophical background on Cantor’s proof and its relation to Russell’s paradox. I’ll then show how techniques developed to treat Russell’s paradox in modal set theory can be generalized to produce set theories consistent with the idea that there’s only one size of infinity.
- - - - Tuesday, Sep 15, 2020 - - - -
- - - - Wednesday, Sep 16, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, Sep 16, 5:00pm
The seminar will take place virtually at 5pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
TBA
- - - - Thursday, Sep 17, 2020 - - - -
- - - - Friday, Sep 18, 2020 - - - -
UA and the Number of Normal Measures over ℵω+1
The Ultrapower Axiom UA, introduced by Goldberg and Woodin, is known to have many striking consequences. In particular, Goldberg has shown that assuming UA, the Mitchell ordering of normal measures over a measurable cardinal is linear. I will discuss how this result may be used to construct choiceless models of ZF in which the number of normal measures at successors of singular cardinals can be precisely controlled.
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)
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Logic Seminar 9 Sept 2020 17:00 hrs at NUS by Ming Xiao
This Week in Logic
- - - - Monday, Aug 31, 2020 - - - -
- - - - Tuesday, Sep 1, 2020 - - - -
- - - - Wednesday, Sep 02, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, Sep 2, 3:00pm
The seminar will take place virtually at 3pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
September 2
Petr Glivický, Universität Salzburg
The ω-iterated nonstandard extension of N and Ramsey combinatorics
In the theory of nonstandard methods (traditionally known as nonstandard analysis), each mathematical object (a set) x has a uniquely determined so called nonstandard extension ∗x. In general, ∗x⊋{∗y;y∈x} - that is, besides the original 'standard' elements ∗y for y∈x, the set ∗x contains some new 'nonstandard' elements.
For instance, some of the nonstandard elements of ∗R can be interpreted as infinitesimals (there is ε∈∗R such that 0<ε<1/n for all n∈N) allowing for nonstandard analysis to be developed in ∗R, while ∗N turns out to be an (at least ℵ1-saturated) nonstandard elementary extension of N (in the language of arithmetic).
While the whole nonstandard real analysis is most naturally developed in ∗R (with just a few advanced topics where using the second extension ∗∗R is convenient, though far from necessary), recent successful applications of nonstandard methods in combinatorics on N have utilized also higher order extensions (n)∗N=∗∗∗⋯∗N with the chain ∗∗∗⋯∗ of length n>2.
In this talk we are going to study the structure of the ω-iterated nonstandard extension ⋅N=⋃n∈ω(n)∗N of N and show how the obtained results shed new light on the complexities of Ramsey combinatorics on N and allow us to drastically simplify proofs of many advanced Ramsey type theorems such as Hindmann's or Milliken's and Taylor's.
- - - - Thursday, Sep 03, 2020 - - - -
Seminar in philosophical logic
Thursday, Sep 3, 6:30pm
Rohit Parikh, City University of New York
On September 3 I will give a talk in the Zoom seminar in philosophical logic which takes place on Thursdays at 6:30 PM.
I will speak about the Sorites paradox and vagueness, relying on previous work by Michael Dummett, Kit Fine, Lotfi Zadeh and myself. I hope you will find it enjoyable.
- - - - Friday, Sep 04, 2020 - - - -
On logics that make a bridge from the Discrete to the Continuous
We study logics which model the passage between an infinite sequence of finite models to an uncountable limiting object, such as is the case in the context of graphons. Of particular interest is the connection between the countable and the uncountable object that one obtains as the union versus the combinatorial limit of the same sequence.
Next Week in Logic at CUNY:
- - - - Monday, Sep 7, 2020 - - - -
- - - - Tuesday, Sep 8, 2020 - - - -
- - - - Wednesday, Sep 9, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, Sep 9, 3:00pm
The seminar will take place virtually at 3pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Saeideh Bahrami, Institute for Research in Fundamental Sciences, TehranFixed Points of Initial Self-Embeddings of Models of Arithmetic
In 1973, Harvey Friedman proved his striking result on initial self-embeddings of countable nonstandard models of set theory and Peano arithmetic. In this talk, I will discuss my joint work with Ali Enayat focused on the fixed point set of initial self-embeddings of countable nonstandard models of arithmetic. Especially, I will survey the proof of some generalizations of well-known results on the fixed point set of automorphisms of countable recursively saturated models of PA, to results about the fixed point set of initial self-embeddings of countable nonstandard models of IΣ1.
- - - - Thursday, Sep 10, 2020 - - - -
- - - - Friday, Sep 11, 2020 - - - -
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
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Wednesday seminar
Logic Seminar 26 Aug 2020 17:00 hrs at NUS
Logic Seminar Login Details
Logic Seminar 19 August 2020 17:00 hrs at NUS (Zoom)
Wednesday seminar
Logic Seminar 19 August 2020 17:00 hrs at NUS (Zoom)
Logic Seminar Wed 12 August 2020 17:00 hrs at NUS
Wednesday seminar
Wednesday seminar
This Week in Logic at CUNY
- - - - Monday, Jul 27, 2020 - - - -
- - - - Tuesday, Jul 28, 2020 - - - -
- - - - Wednesday, Jul 29, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, July 29, 7:00pm
The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Kameryn Williams, University of Hawai‘i at Mānoa
End-extensions of models of set theory and the Σ1 universal finite sequence
Recall that if M⊆N are models of set theory then N end-extends M if N does not have new elements for sets in M. In this talk I will discuss a Σ1-definable finite sequence which is universal for end extensions in the following sense. Consider a computably axiomatizable extension ¯¯¯¯¯¯¯ZF of ZF. There is a Σ1-definable finite sequencea0,a1,…,anwith the following properties.
* ZF proves that the sequence is finite.
* In any transitive model of ¯¯¯¯¯¯¯ZF the sequence is empty.
* If M is a countable model of ¯¯¯¯¯¯¯ZF in which the sequence is s and t∈M is a finite sequence extending s then there is an end-extension N⊨¯¯¯¯¯¯¯ZF of M in which the sequence is exactly t.
* Indeed, for the previous statements it suffices that M⊨ZF and end-extends a submodel W⊨¯¯¯¯¯¯¯ZF of height at least (ωL1)M.
This universal finite sequence can be used to determine the modal validities of end-extensional set-theoretic potentialism, namely to be exactly the modal theory S4. The sequence can also be used to show that every countable model of set theory extends to a model satisfying the end-extensional maximality principle, asserting that any possibly necessary sentence is already true.
This talk is about joint work with Joel David Hamkins. The Σ1 universal finite sequence is a sister to the Σ2 universal finite sequence for rank-extensions of Hamkins and Woodin, and both are cousins of Woodin's universal algorithm for arithmetic.
- - - - Friday, Jul 31, 2020 - - - -
Dissertation defense: Alternative Cichoń diagrams and forcing axioms compatible with CH
This dissertation surveys several topics in the general areas of iterated forcing, infinite combinatorics and set theory of the reals. There are two parts. In the first half I consider alternative versions of the Cichoń diagram. First I show that for a wide variety of reduction concepts there is a Cichoń diagram for effective cardinal characteristics relativized to that reduction. As an application I investigate in detail the Cichoń diagram for degrees of constructibility relative to a fixed inner model of ZFC. Then I study generalizations of cardinal characteristics to the space of functions from ωω to ωω. I prove that these cardinals can be organized into two diagrams analogous to the standard Cichoń diagram show several independence results and investigate their relation to cardinal invariants on omega. In the second half of the thesis I look at forcing axioms compatible with CH. First I consider Jensen's subcomplete and subproper forcing. I generalize these notions to larger classes which are (apparently) much more nicely behaved structurally. I prove iteration and preservation theorems for both classes and use these to produce many new models of the subcomplete forcing axiom. Finally I deal with dee-complete forcing and its associated axiom DCFA. Extending a well-known result of Shelah, I show that if a tree of height ω1 with no branch can be embedded into an ω1 tree, possibly with uncountable branches, then it can be specialized without adding reals. As a consequence I show that DCFA implies there are no Kurepa trees, even if CH fails.
- - - - Monday, Aug 3, 2020 - - - -
- - - - Tuesday, Aug 4, 2020 - - - -
- - - - Wednesday, Aug 5, 2020 - - - -
- - - - Thursday, Aug 6, 2020 - - - -
- - - - Friday, Aug 7, 2020 - - - -
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)
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Wednesday seminar
Logic summer school at Fudan University, August 10-21, 2020
This Week in Logic at CUNY
- - - - Monday, Jul 20, 2020 - - - -
- - - - Tuesday, Jul 21, 2020 - - - -
- - - - Wednesday, Jul 22, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, July 22, 8:00pm
The seminar will take place virtually at 8pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Tin Lok Wong, National University of Singapore
Properties preserved in cofinal extensions
Cofinal extensions generally preserve many more properties of a model of arithmetic than their sisters, end extensions. Exactly how much must or can they preserve? The answer is intimately related to how much arithmetic the model can do. I will survey what is known and what is not known about this question, and report on some recent work on this line.
- - - - Friday, Jul 24, 2020 - - - -
Measurable cardinals and limits in the category of sets
An old result of Isbell characterises measurable cardinals in terms of certain canonical limits in the category of sets. After introducing this characterisation, I will talk about recent work with Adamek, Campion, Positselski and Rosicky teasing out the importance of the canonicity for this and related results. The language will be category-theoretic but the proofs will be quite hands-on combinatorial constructions with sets.
Next Week in Logic at CUNY:
- - - - Monday, Jul 27, 2020 - - - -
- - - - Tuesday, Jul 28, 2020 - - - -
- - - - Wednesday, Jul 29, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, July 29, 7:00pm
The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Kameryn Williams, University of Hawai‘i at Mānoa
End-extensions of models of set theory and the Σ1 universal finite sequence
Recall that if M⊆N are models of set theory then N end-extends M if N does not have new elements for sets in M. In this talk I will discuss a Σ1-definable finite sequence which is universal for end extensions in the following sense. Consider a computably axiomatizable extension ¯¯¯¯¯¯¯ZF of ZF. There is a Σ1-definable finite sequencea0,a1,…,anwith the following properties.
* ZF proves that the sequence is finite.
* In any transitive model of ¯¯¯¯¯¯¯ZF the sequence is empty.
* If M is a countable model of ¯¯¯¯¯¯¯ZF in which the sequence is s and t∈M is a finite sequence extending s then there is an end-extension N⊨¯¯¯¯¯¯¯ZF of M in which the sequence is exactly t.
* Indeed, for the previous statements it suffices that M⊨ZF and end-extends a submodel W⊨¯¯¯¯¯¯¯ZF of height at least (ωL1)M.
This universal finite sequence can be used to determine the modal validities of end-extensional set-theoretic potentialism, namely to be exactly the modal theory S4. The sequence can also be used to show that every countable model of set theory extends to a model satisfying the end-extensional maximality principle, asserting that any possibly necessary sentence is already true.
This talk is about joint work with Joel David Hamkins. The Σ1 universal finite sequence is a sister to the Σ2 universal finite sequence for rank-extensions of Hamkins and Woodin, and both are cousins of Woodin's universal algorithm for arithmetic.
- - - - Friday, Jul 31, 2020 - - - -
Dissertation defense: Alternative Cichoń diagrams and forcing axioms compatible with CH
This dissertation surveys several topics in the general areas of iterated forcing, infinite combinatorics and set theory of the reals. There are two parts. In the first half I consider alternative versions of the Cichoń diagram. First I show that for a wide variety of reduction concepts there is a Cichoń diagram for effective cardinal characteristics relativized to that reduction. As an application I investigate in detail the Cichoń diagram for degrees of constructibility relative to a fixed inner model of ZFC. Then I study generalizations of cardinal characteristics to the space of functions from ωω to ωω. I prove that these cardinals can be organized into two diagrams analogous to the standard Cichoń diagram show several independence results and investigate their relation to cardinal invariants on omega. In the second half of the thesis I look at forcing axioms compatible with CH. First I consider Jensen's subcomplete and subproper forcing. I generalize these notions to larger classes which are (apparently) much more nicely behaved structurally. I prove iteration and preservation theorems for both classes and use these to produce many new models of the subcomplete forcing axiom. Finally I deal with dee-complete forcing and its associated axiom DCFA. Extending a well-known result of Shelah, I show that if a tree of height ω1 with no branch can be embedded into an ω1 tree, possibly with uncountable branches, then it can be specialized without adding reals. As a consequence I show that DCFA implies there are no Kurepa trees, even if CH fails.
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
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If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Wednesday seminar
Wednesday seminar
This Week in Logic at CUNY
- - - - Tuesday, Jul 7, 2020 - - - -
- - - - Wednesday, Jul 8, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, July 8, 7:00pm
The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Corey Switzer, CUNY
Axiomatizing Kaufmann models in strong logics
A Kaufmann model is an ω1-like, recursively saturated, rather classless model of PA. Such models were constructed by Kaufmann under the ♢ assumption and then shown to exist in ZFC by Shelah using an absoluteness argument involving the logic Lω1,ω(Q) where Q is the quantifier 'there exists uncountably many…'. It remains an intriguing, if vague, open problem whether one can construct a Kaufmann model in ZFC 'by hand' i.e. without appealing to some form of absoluteness or other very non-constructive methods. In this talk I consider the related problem of axiomatizing Kaufmann models in Lω1,ω(Q) and show that this is independent of ZFC. Along the way we'll see that it is also independent of ZFC whether there is an ω1-preserving forcing notion adding a truth predicate to a Kaufmann model.
- - - - Thursday, Jul 9, 2020 - - - -
- - - - Friday, Jul 10, 2020 - - - -
Uniform large cardinal characterizations and ideals up to measurability
- - - - Monday, Jul 13, 2020 - - - -
- - - - Tuesday, Jul 14, 2020 - - - -
- - - - Wednesday, Jul 15, 2020 - - - -
- - - - Thursday, Jul 16, 2020 - - - -
- - - - Friday, Jul 17, 2020 - - - -
Kaethe Minden Bard College at Simon's Rock
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
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If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Wednesday seminar
No seminar this week
Wednesday seminar
This Week in Logic at CUNY
- - - - Tuesday, Jun 30, 2020 - - - -
- - - - Wednesday, Jul 1, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, July 1, 7:00pm
The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Zachiri McKenzie,
Initial self-embeddings of models of set theory: Part II
In the 1973 paper 'Countable models of set theory', H. Friedman's investigation of embeddings between countable models of subsystems of ZF yields the following two striking results:
1. Every countable nonstandard model of PA is isomorphic to a proper initial segment of itself.
2. Every countable nonstandard model of a sufficiently strong subsystem of ZF is isomorphic to a proper initial segment that is a union of ranks of the original model.
Note that, in contrast to PA, in the context of set theory there are three alternative notions of 'initial segment': transitive subclass, transitive subclass that is closed under subsets and rank-initial segment. Paul Gorbow, in his Ph.D. thesis, systematically studies versions of H. Friedman's self-embedding that yield isomorphisms between a countable nonstandard model of set theory and a rank-initial segment of itself. In these two talks I will discuss recent joint work with Ali Enayat that investigates models of set theory that are isomorphic to a transitive subclass of itself. We call the maps witnessing these isomorphisms 'initial self-embeddings'. I will outline a proof of a refinement of H. Friedman's Theorem that guarantees the existence of initial self-embeddings for certain subsystems of ZF without the powerset axiom. I will then discuss several examples including a nonstandard model of ZFC minus the powerset axiom that admits no initial self-embedding, and models that separate the three different notions of self-embedding for models of set theory. Finally, I will discuss two interesting applications of our version of H. Freidman's Theorem. The first of these is a refinement of a result due to Quinsey that guarantees the existence of partially elementary proper transitive subclasses of non-standard models of ZF minus the powerset axiom. The second result shows that every countable model of ZF with a nonstandard natural number is isomorphic to a transitive subclass of the hereditarily countable sets of its own constructible universe.
- - - - Friday, Jul 3, 2020 - - - -
We will discuss some recent ZFC results concerning the generalized Baire spaces, and more specifically the generalized bounding number, relatives of the generalized almost disjointness number, as well as generalized reaping and domination.
- - - - Monday, Jul 6, 2020 - - - -
- - - - Tuesday, Jul 7, 2020 - - - -
- - - - Wednesday, Jul 8, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, July 8, 7:00pm
The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Corey Switzer, CUNY
Axiomatizing Kaufmann models in strong logics
A Kaufmann model is an ω1-like, recursively saturated, rather classless model of PA. Such models were constructed by Kaufmann under the ♢ assumption and then shown to exist in ZFC by Shelah using an absoluteness argument involving the logic Lω1,ω(Q) where Q is the quantifier 'there exists uncountably many…'. It remains an intriguing, if vague, open problem whether one can construct a Kaufmann model in ZFC 'by hand' i.e. without appealing to some form of absoluteness or other very non-constructive methods. In this talk I consider the related problem of axiomatizing Kaufmann models in Lω1,ω(Q) and show that this is independent of ZFC. Along the way we'll see that it is also independent of ZFC whether there is an ω1-preserving forcing notion adding a truth predicate to a Kaufmann model.
- - - - Thursday, Jul 9, 2020 - - - -
- - - - Friday, Jul 10, 2020 - - - -
TBA
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
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If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
This Week in Logic at CUNY
- - - - Tuesday, Jun 23, 2020 - - - -
- - - - Wednesday, Jun 24, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, June 24, 2:00pm NOTE: 2:00pm START TIME
The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.Bartosz Wcisło, Polish Academy of Sciences
Tarski boundary III
Truth theories investigate the notion of truth using axiomatic methods. To a fixed base theory (typically Peano Arithmetic PA) we add a unary predicate T(x) with the intended interpretation 'x is a (code of a) true sentence.' Then we analyse how adding various possible sets of axioms for that predicate affects its behaviour.
One of the aspects which we are trying to understand is which truth-theoretic principles make the added truth predicate 'strong' in that the resulting theory is not conservative over the base theory. Ali Enayat proposed to call this demarcating line between conservative and non-conservative truth theories 'the Tarski boundary.'
Research on Tarski boundary revealed that natural truth theoretic principles extending compositional axioms tend to be either conservative over PA or exactly equivalent to the principle of global reflection over A. It says that sentences provable in PA are true in the sense of the predicate T. This in turn is equivalent to Δ0 induction for the compositional truth predicate which turns out to be a surprisingly robust theory.
The equivalences between nonconservative truth theories are typically proved by relatively direct ad hoc arguments. However, certain patterns seem common to these proofs. The first one is construction of various arithmetical partial truth predicates which provably in a given theory have better properties than the original truth predicate. The second one is deriving induction for these truth predicates from internal induction, a principle which says that for any arithmetical formula, the set of those elements for which that formula is satisfied under the truth predicate satisfies the usual induction axioms.
As an example of this phenomenon, we will present two proofs. First, we will show that global reflection principle is equivalent to local induction. Global reflection expresses that any sentence provable in PA is true. Local induction says that any predicate obtained by restricting truth predicate to sentences of a fixed syntactic complexity c satisfies full induction. This is an observation due to Mateusz Łełyk and the author of this presentation.
The second example is a result by Ali Enayat who showed that CT0, a theory compositional truth with Δ0 induction, is arithmetically equivalent to the theory of compositional truth together with internal induction and disjunctive correctness.
This talk is intended as a continuation of 'Tarski boundary II' presentation at the same seminar. However, we will try to avoid excessive assumptions on familiarity with the previous part.
- - - - Thursday, Jun 25, 2020 - - - -
- - - - Friday, Jun 26, 2020 - - - -
Joel David Hamkins, Oxford University
Categorical cardinals
Zermelo famously characterized the models of second-order Zermelo-Fraenkel set theory ZFC2 in his 1930 quasi-categoricity result asserting that the models of ZFC2 are precisely those isomorphic to a rank-initial segment Vκ of the cumulative set-theoretic universe V cut off at an inaccessible cardinal κ. I shall discuss the extent to which Zermelo's quasi-categoricity analysis can rise fully to the level of categoricity, in light of the observation that many of the Vκ universes are categorically characterized by their sentences or theories. For example, if κ is the smallest inaccessible cardinal, then up to isomorphism Vκ is the unique model of ZFC2 plus the sentence 'there are no inaccessible cardinals.' This cardinal κ is therefore an instance of what we call a first-order sententially categorical cardinal. Similarly, many of the other inaccessible universes satisfy categorical extensions of ZFC2 by a sentence or theory, either in first or second order. I shall thus introduce and investigate the categorical cardinals, a new kind of large cardinal. This is joint work with Robin Solberg (Oxford).
- - - - Monday, Jun 29, 2020 - - - -
- - - - Tuesday, Jun 30, 2020 - - - -
- - - - Wednesday, Jul 1, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, July 1, 7:00pm
The seminar will take place virtually at 7pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.
Zachiri McKenzie,
Initial self-embeddings of models of set theory: Part II
In the 1973 paper 'Countable models of set theory', H. Friedman's investigation of embeddings between countable models of subsystems of ZF yields the following two striking results:
1. Every countable nonstandard model of PA is isomorphic to a proper initial segment of itself.
2. Every countable nonstandard model of a sufficiently strong subsystem of ZF is isomorphic to a proper initial segment that is a union of ranks of the original model.
Note that, in contrast to PA, in the context of set theory there are three alternative notions of 'initial segment': transitive subclass, transitive subclass that is closed under subsets and rank-initial segment. Paul Gorbow, in his Ph.D. thesis, systematically studies versions of H. Friedman's self-embedding that yield isomorphisms between a countable nonstandard model of set theory and a rank-initial segment of itself. In these two talks I will discuss recent joint work with Ali Enayat that investigates models of set theory that are isomorphic to a transitive subclass of itself. We call the maps witnessing these isomorphisms 'initial self-embeddings'. I will outline a proof of a refinement of H. Friedman's Theorem that guarantees the existence of initial self-embeddings for certain subsystems of ZF without the powerset axiom. I will then discuss several examples including a nonstandard model of ZFC minus the powerset axiom that admits no initial self-embedding, and models that separate the three different notions of self-embedding for models of set theory. Finally, I will discuss two interesting applications of our version of H. Freidman's Theorem. The first of these is a refinement of a result due to Quinsey that guarantees the existence of partially elementary proper transitive subclasses of non-standard models of ZF minus the powerset axiom. The second result shows that every countable model of ZF with a nonstandard natural number is isomorphic to a transitive subclass of the hereditarily countable sets of its own constructible universe.
- - - - Friday, Jul 3, 2020 - - - -
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
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Set theory seminar this week: Will Brian
Wednesday seminar
Set theory seminar this week: David Schrittesser
Abstract: The notion of mad family can be generalized by replacing the finite ideal by an iterated Fubini product of the finite ideal. While these ideals are more complicated both combinatorially and in terms of Borel complexity, it turns out that the same assumptions of Ramsey theoretic regularity can rule out their existence. We sketch a proof of this and some related results. This talk is a sequel to my last talk at the Fields Institute Seminar.
This Week in Logic at CUNY
- - - - Tuesday, Jun 16, 2020 - - - -
- - - - Wednesday, Jun 17, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, June 17, 2:00pm NOTE: 2:00pm START TIME
The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.Mateusz Łełyk, University of Warsaw
Partial Reflection over Uniform Disquotational Truth
In the context of arithmetic, a reflection principle for a theory Th is a formal way of expressing that all theorems of Th are true. In the presence of a truth predicate for the language of Th this principle can be expressed as a single sentence (called the Global Reflection principle over Th) but most often is met in the form of a scheme consisting of all sentences of the form
This perspective is nowadays very fruitfully exploited in the context of formal theories of truth. One of the most basic observations is that strong axioms for the notions of truth follow from formally weak types of axiomatizations modulo reflection principles. In such a way compositional axioms are consequences of the uniform disquotational scheme for for the truth predicate, which is
The above observation is also used in the recent approach to ordinal analysis of theories of predicative strength by Lev Beklemishev and Fedor Pakhomov. The assignment of ordinal notations to theories proceeds via partial reflection principles (for formulae of a fixed Σn complexity) over (iterated) disquotational scheme. It becomes important to relate theories of this form to fragments of standard theories of truth, in particular the ones based on induction for restricted classes of formulae such as CT0 (the theory of compositional truth with Δ0-induction for the extended language. The theory was discussed at length in Bartek Wcisło's talk). Beklemishev and Pakhomov leave the following open question:
The main goal of our talk is to present the proof of the affirmative answer to this question. The result significantly improves the known fact on the provability of Global Reflection over PA in CT0. During the talk, we explain the theoretical context described above including the information on how the result fits into Beklemishev-Pakhomov project. In the meantime we give a different proof of their characterisation of Δ0-reflection over the disquotational scheme.
Despite the proof-theoretical flavour of these results, our proofs rests on essentially model-theoretical techniques. The important ingredient is the Arithmetized Completeness Theorem.
- - - - Thursday, Jun 18, 2020 - - - -
- - - - Friday, Jun 19, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, June 19, 2pm
Strong guessing models
The notion of a guessing model introduced by Viale and Weiss. The principle GM(ω2,ω1) asserts that there are stationary many guessing models of size ℵ1 in Hθ, for all large enough regular θ. It follows from PFA and implies many of its structural consequences, however it does not settle the value of the continuum. In search of higher of forcing axioms it is therefore natural to look for extensions and higher versions of this principle. We formulate and prove the consistency of one such statement that we call SGM+(ω3,ω1).
It has a number of important structural consequences:
- the tree property at ℵ2 and ℵ3
- the failure of various weak square principles
- the Singular Cardinal Hypothesis
- Mitchell’s Principle: the approachability ideal agrees with the non stationary ideal on the set of cof(ω1) ordinals in ω2
- Souslin’s Hypothesis
- The negation of the weak Kurepa Hypothesis
- Abraham’s Principles: every forcing which adds a subset of ω2 either adds a real or collapses some cardinals, etc.
The results are joint with my PhD students Rahman Mohammadpour.
- - - - Monday, Jun 22, 2020 - - - -
- - - - Tuesday, Jun 23, 2020 - - - -
- - - - Wednesday, Jun 24, 2020 - - - -
- - - - Thursday, Jun 25, 2020 - - - -
- - - - Friday, Jun 26, 2020 - - - -
Joel David Hamkins, Oxford University
TBA
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Wednesday seminar
Set theory seminar this week: Jamal Kawach
This Week in Logic at CUNY
- - - - Tuesday, Jun 9, 2020 - - - -
- - - - Wednesday, Jun 10, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, June 10, 7:00pm
Initial self-embeddings of models of set theory: Part II
In the 1973 paper 'Countable models of set theory', H. Friedman's investigation of embeddings between countable models of subsystems of ZF yields the following two striking results:
1. Every countable nonstandard model of PA is isomorphic to a proper initial segment of itself.
2. Every countable nonstandard model of a sufficiently strong subsystem of ZF is isomorphic to a proper initial segment that is a union of ranks of the original model.
Note that, in contrast to PA, in the context of set theory there are three alternative notions of 'initial segment': transitive subclass, transitive subclass that is closed under subsets and rank-initial segment. Paul Gorbow, in his Ph.D. thesis, systematically studies versions of H. Friedman's self-embedding that yield isomorphisms between a countable nonstandard model of set theory and a rank-initial segment of itself. In these two talks I will discuss recent joint work with Ali Enayat that investigates models of set theory that are isomorphic to a transitive subclass of itself. We call the maps witnessing these isomorphisms 'initial self-embeddings'. I will outline a proof of a refinement of H. Friedman's Theorem that guarantees the existence of initial self-embeddings for certain subsystems of ZF without the powerset axiom. I will then discuss several examples including a nonstandard model of ZFC minus the powerset axiom that admits no initial self-embedding, and models that separate the three different notions of self-embedding for models of set theory. Finally, I will discuss two interesting applications of our version of H. Freidman's Theorem. The first of these is a refinement of a result due to Quinsey that guarantees the existence of partially elementary proper transitive subclasses of non-standard models of ZF minus the powerset axiom. The second result shows that every countable model of ZF with a nonstandard natural number is isomorphic to a transitive subclass of the hereditarily countable sets of its own constructible universe.
- - - - Thursday, Jun 11, 2020 - - - -
- - - - Friday, Jun 12, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, June 12, 2pm
Michał Godziszewski, Munich Center for Mathematical Philosophy
The Multiverse, Recursive Saturation and Well-Foundedness Mirage: Part II
Recursive saturation, introduced by J. Barwise and J. Schlipf is a robust notion which has proved to be important for the study of nonstandard models (in particular, it is ubiquitous in the model theory of axiomatic theories of truth, e.g. in the topic of satisfaction classes, where one can show that if M⊨ZFC is a countable ω-nonstandard model, then M admits a satisfaction class iff M is recursively saturated). V. Gitman and J. Hamkins showed in A Natural Model of the Multiverse Axioms that the collection of countable, recursively saturated models of set theory satisfy the so-called Hamkins's Multiverse Axioms. The property that forces all the models in the Multiverse to be recursively saturated is the so-called Well-Foundedness Mirage axiom which asserts that every universe is ω-nonstandard from the perspective of some larger universe, or to be more precise, that: if a model M is in the multiverse then there is a model N in the multiverse such that M is a set in N and N⊨′M is ω−nonstandard.'. Inspection of the proof led to a question if the recursive saturation could be avoided in the Multiverse by weakening the Well-Foundedness Mirage axiom. Our main results answer this in the positive. We give two different versions of the Well-Foundedness Mirage axiom - what we call Weak Well-Foundedness Mirage (saying that if M is a model in the Multiverse then there is a model N in the Multiverse such that M∈N and N⊨′M is nonstandard.'.) and Covering Well-Foundedness Mirage (saying that if M is a model in the Multiverse then there is a model N in the Multiverse with K∈N such that K is an end-extension of M and N⊨′K is ω−nonstandard.'). I will present constructions of two different Multiverses satisfying these two weakened axioms. This is joint work with V. Gitman. T. Meadows and K. Williams.
- - - - Monday, Jun 15, 2020 - - - -
- - - - Tuesday, Jun 16, 2020 - - - -
- - - - Wednesday, Jun 17, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, June 17, 2:00pm NOTE: 2:00pm START TIME
The seminar will take place virtually at 2pm New York City Time. Please email Victoria Gitman (vgitman@nylogic.org) for meeting id.Mateusz Łełyk, University of Warsaw
Partial Reflection over Uniform Disquotational Truth
In the context of arithmetic, a reflection principle for a theory Th is a formal way of expressing that all theorems of Th are true. In the presence of a truth predicate for the language of Th this principle can be expressed as a single sentence (called the Global Reflection principle over Th) but most often is met in the form of a scheme consisting of all sentences of the form
This perspective is nowadays very fruitfully exploited in the context of formal theories of truth. One of the most basic observations is that strong axioms for the notions of truth follow from formally weak types of axiomatizations modulo reflection principles. In such a way compositional axioms are consequences of the uniform disquotational scheme for for the truth predicate, which is
The above observation is also used in the recent approach to ordinal analysis of theories of predicative strength by Lev Beklemishev and Fedor Pakhomov. The assignment of ordinal notations to theories proceeds via partial reflection principles (for formulae of a fixed Σn complexity) over (iterated) disquotational scheme. It becomes important to relate theories of this form to fragments of standard theories of truth, in particular the ones based on induction for restricted classes of formulae such as CT0 (the theory of compositional truth with Δ0-induction for the extended language. The theory was discussed at length in Bartek Wcisło's talk). Beklemishev and Pakhomov leave the following open question:
The main goal of our talk is to present the proof of the affirmative answer to this question. The result significantly improves the known fact on the provability of Global Reflection over PA in CT0. During the talk, we explain the theoretical context described above including the information on how the result fits into Beklemishev-Pakhomov project. In the meantime we give a different proof of their characterisation of Δ0-reflection over the disquotational scheme.
Despite the proof-theoretical flavour of these results, our proofs rests on essentially model-theoretical techniques. The important ingredient is the Arithmetized Completeness Theorem.
- - - - Thursday, Jun 18, 2020 - - - -
- - - - Friday, Jun 19, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, June 19, 2pm
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
- - - - Tuesday, Jun 2, 2020 - - - -
- - - - Wednesday, Jun 3, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, June 3, 7:00pm
Zachiri McKenzie,
Initial self-embeddings of models of set theory: Part I
In the 1973 paper 'Countable models of set theory', H. Friedman's investigation of embeddings between countable models of subsystems of ZF yields the following two striking results:
1. Every countable nonstandard model of PA is isomorphic to a proper initial segment of itself.
2. Every countable nonstandard model of a sufficiently strong subsystem of ZF is isomorphic to a proper initial segment that is a union of ranks of the original model.
Note that, in contrast to PA, in the context of set theory there are three alternative notions of 'initial segment': transitive subclass, transitive subclass that is closed under subsets and rank-initial segment. Paul Gorbow, in his Ph.D. thesis, systematically studies versions of H. Friedman's self-embedding that yield isomorphisms between a countable nonstandard model of set theory and a rank-initial segment of itself. In these two talks I will discuss recent joint work with Ali Enayat that investigates models of set theory that are isomorphic to a transitive subclass of itself. We call the maps witnessing these isomorphisms 'initial self-embeddings'. I will outline a proof of a refinement of H. Friedman's Theorem that guarantees the existence of initial self-embeddings for certain subsystems of ZF without the powerset axiom. I will then discuss several examples including a nonstandard model of ZFC minus the powerset axiom that admits no initial self-embedding, and models that separate the three different notions of self-embedding for models of set theory. Finally, I will discuss two interesting applications of our version of H. Freidman's Theorem. The first of these is a refinement of a result due to Quinsey that guarantees the existence of partially elementary proper transitive subclasses of non-standard models of ZF minus the powerset axiom. The second result shows that every countable model of ZF with a nonstandard natural number is isomorphic to a transitive subclass of the hereditarily countable sets of its own constructible universe.
- - - - Thursday, Jun 4, 2020 - - - -
- - - - Friday, Jun 5, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, June 5, 2pm
TBA
- - - - Monday, Jun 8, 2020 - - - -
- - - - Tuesday, Jun 9, 2020 - - - -
- - - - Wednesday, Jun 10, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, June 10, 7:00pm
Initial self-embeddings of models of set theory: Part II
In the 1973 paper 'Countable models of set theory', H. Friedman's investigation of embeddings between countable models of subsystems of ZF yields the following two striking results:
1. Every countable nonstandard model of PA is isomorphic to a proper initial segment of itself.
2. Every countable nonstandard model of a sufficiently strong subsystem of ZF is isomorphic to a proper initial segment that is a union of ranks of the original model.
Note that, in contrast to PA, in the context of set theory there are three alternative notions of 'initial segment': transitive subclass, transitive subclass that is closed under subsets and rank-initial segment. Paul Gorbow, in his Ph.D. thesis, systematically studies versions of H. Friedman's self-embedding that yield isomorphisms between a countable nonstandard model of set theory and a rank-initial segment of itself. In these two talks I will discuss recent joint work with Ali Enayat that investigates models of set theory that are isomorphic to a transitive subclass of itself. We call the maps witnessing these isomorphisms 'initial self-embeddings'. I will outline a proof of a refinement of H. Friedman's Theorem that guarantees the existence of initial self-embeddings for certain subsystems of ZF without the powerset axiom. I will then discuss several examples including a nonstandard model of ZFC minus the powerset axiom that admits no initial self-embedding, and models that separate the three different notions of self-embedding for models of set theory. Finally, I will discuss two interesting applications of our version of H. Freidman's Theorem. The first of these is a refinement of a result due to Quinsey that guarantees the existence of partially elementary proper transitive subclasses of non-standard models of ZF minus the powerset axiom. The second result shows that every countable model of ZF with a nonstandard natural number is isomorphic to a transitive subclass of the hereditarily countable sets of its own constructible universe.
- - - - Thursday, Jun 11, 2020 - - - -
- - - - Friday, Jun 12, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, June 12, 2pm
TBA
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
UPDATE - This Week in Logic at CUNY
- - - - Monday, May 25, 2020 - - - -
- - - - Tuesday, May 26, 2020 - - - -
- - - - Wednesday, May 27, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, May 27, 2:00pm
Bartosz Wcisło, University of Warsaw
Tarski boundary II
Truth theories investigate the notion of truth with axiomatic methods. To a fixed base theory (typically Peano Arithmetic PA) we add a unary predicate T(x) with the intended interpretation 'x is a (code of a) true sentence.' Then we analyse how adding various possible sets of axioms for that predicate affects its behaviour.
One of the aspects we are trying to understand is which truth-theoretic principles make the added truth predicate 'strong' in that the resulting theory is not conservative over the base theory. Ali Enayat proposed to call this 'demarcating line' between conservative and non-conservative truth theories 'the Tarski boundary.'
Research on Tarski boundary revealed that natural truth theoretic principles extending compositional axioms tend to be either conservative over PA or exactly equivalent to the principle of global reflection over PA. It says that sentences provable in PA are true in the sense of the predicate T. This in turn is equivalent to Δ0 induction for the compositional truth predicate which turns out to be a surprisingly robust theory.
In our talk, we will try to sketch proofs representative of research on Tarski boundary. We will present the proof by Enayat and Visser showing that the compositional truth predicate is conservative over PA. We will also try to discuss how this proof forms a robust basis for further conservativeness results.
On the non-conservative side of Tarski boundary, the picture seems less organised, since more arguments are based on ad hoc constructions. However, we will try to show some themes which occur rather repeatedly in these proofs: iterated truth predicates and the interplay between properties of good truth-theoretic behaviour and induction. To this end, we will present the argument that disjunctive correctness together with the internal induction principle for a compositional truth predicate yields the same consequences as Δ0-induction for the compositional truth predicate (as proved by Ali Enayat) and that it shares arithmetical consequences with global reflection. The presented results are currently known to be suboptimal.
This talk is intended as a continuation of 'Tarski boundary' presentation. However, we will try to avoid excessive assumptions on familiarity with the previous part.
- - - - Thursday, May 28, 2020 - - - -
- - - - Friday, May 29, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, May 29, 2pm
The geology of inner mantles
In this talk I will present some results about the sequence of inner mantles, answering some questions of Fuchs, Hamkins, and Reitz. Specifically, I will present the following results, analogues of classic results about the sequence of iterated HODs.
1. (Joint with Reitz) Consider a model of set theory and consider an ordinal eta in that model. Then this model has a class forcing extension whose eta-th inner mantle is the model we started out with, where the sequence of inner mantles does not stabilize before eta.
2. It is consistent that the omega-th inner mantle is an inner model of ZF + ¬AC.
3. It is consistent that the omega-th inner mantle is not a definable class, and indeed fails to satisfy Collection.
- - - - Monday, Jun 1, 2020 - - - -
- - - - Tuesday, Jun 2, 2020 - - - -
- - - - Wednesday, Jun 3, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, June 3, 7:00pm
Zachiri McKenzie,
Initial self-embeddings of models of set theory: Part I
In the 1973 paper 'Countable models of set theory', H. Friedman's investigation of embeddings between countable models of subsystems of ZF yields the following two striking results:
1. Every countable nonstandard model of PA is isomorphic to a proper initial segment of itself.
2. Every countable nonstandard model of a sufficiently strong subsystem of ZF is isomorphic to a proper initial segment that is a union of ranks of the original model.
Note that, in contrast to PA, in the context of set theory there are three alternative notions of 'initial segment': transitive subclass, transitive subclass that is closed under subsets and rank-initial segment. Paul Gorbow, in his Ph.D. thesis, systematically studies versions of H. Friedman's self-embedding that yield isomorphisms between a countable nonstandard model of set theory and a rank-initial segment of itself. In these two talks I will discuss recent joint work with Ali Enayat that investigates models of set theory that are isomorphic to a transitive subclass of itself. We call the maps witnessing these isomorphisms 'initial self-embeddings'. I will outline a proof of a refinement of H. Friedman's Theorem that guarantees the existence of initial self-embeddings for certain subsystems of ZF without the powerset axiom. I will then discuss several examples including a nonstandard model of ZFC minus the powerset axiom that admits no initial self-embedding, and models that separate the three different notions of self-embedding for models of set theory. Finally, I will discuss two interesting applications of our version of H. Freidman's Theorem. The first of these is a refinement of a result due to Quinsey that guarantees the existence of partially elementary proper transitive subclasses of non-standard models of ZF minus the powerset axiom. The second result shows that every countable model of ZF with a nonstandard natural number is isomorphic to a transitive subclass of the hereditarily countable sets of its own constructible universe.
- - - - Thursday, Jun 4, 2020 - - - -
- - - - Friday, Jun 5, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, June 5, 2pm
TBA
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
This Week in Logic at CUNY
- - - - Monday, May 25, 2020 - - - -
- - - - Tuesday, May 26, 2020 - - - -
- - - - Wednesday, May 27, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, May 27, 7:00pm
Bartosz Wcisło, University of Warsaw
Tarski boundary II
Truth theories investigate the notion of truth with axiomatic methods. To a fixed base theory (typically Peano Arithmetic PA) we add a unary predicate T(x) with the intended interpretation 'x is a (code of a) true sentence.' Then we analyse how adding various possible sets of axioms for that predicate affects its behaviour.
One of the aspects we are trying to understand is which truth-theoretic principles make the added truth predicate 'strong' in that the resulting theory is not conservative over the base theory. Ali Enayat proposed to call this 'demarcating line' between conservative and non-conservative truth theories 'the Tarski boundary.'
Research on Tarski boundary revealed that natural truth theoretic principles extending compositional axioms tend to be either conservative over PA or exactly equivalent to the principle of global reflection over PA. It says that sentences provable in PA are true in the sense of the predicate T. This in turn is equivalent to Δ0 induction for the compositional truth predicate which turns out to be a surprisingly robust theory.
In our talk, we will try to sketch proofs representative of research on Tarski boundary. We will present the proof by Enayat and Visser showing that the compositional truth predicate is conservative over PA. We will also try to discuss how this proof forms a robust basis for further conservativeness results.
On the non-conservative side of Tarski boundary, the picture seems less organised, since more arguments are based on ad hoc constructions. However, we will try to show some themes which occur rather repeatedly in these proofs: iterated truth predicates and the interplay between properties of good truth-theoretic behaviour and induction. To this end, we will present the argument that disjunctive correctness together with the internal induction principle for a compositional truth predicate yields the same consequences as Δ0-induction for the compositional truth predicate (as proved by Ali Enayat) and that it shares arithmetical consequences with global reflection. The presented results are currently known to be suboptimal.
This talk is intended as a continuation of 'Tarski boundary' presentation. However, we will try to avoid excessive assumptions on familiarity with the previous part.
- - - - Thursday, May 28, 2020 - - - -
- - - - Friday, May 29, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, May 29, 2pm
The geology of inner mantles
In this talk I will present some results about the sequence of inner mantles, answering some questions of Fuchs, Hamkins, and Reitz. Specifically, I will present the following results, analogues of classic results about the sequence of iterated HODs.
1. (Joint with Reitz) Consider a model of set theory and consider an ordinal eta in that model. Then this model has a class forcing extension whose eta-th inner mantle is the model we started out with, where the sequence of inner mantles does not stabilize before eta.
2. It is consistent that the omega-th inner mantle is an inner model of ZF + ¬AC.
3. It is consistent that the omega-th inner mantle is not a definable class, and indeed fails to satisfy Collection.
- - - - Monday, Jun 1, 2020 - - - -
- - - - Tuesday, Jun 2, 2020 - - - -
- - - - Wednesday, Jun 3, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, June 3, 7:00pm
Zachiri McKenzie,
Initial self-embeddings of models of set theory: Part I
In the 1973 paper 'Countable models of set theory', H. Friedman's investigation of embeddings between countable models of subsystems of ZF yields the following two striking results:
1. Every countable nonstandard model of PA is isomorphic to a proper initial segment of itself.
2. Every countable nonstandard model of a sufficiently strong subsystem of ZF is isomorphic to a proper initial segment that is a union of ranks of the original model.
Note that, in contrast to PA, in the context of set theory there are three alternative notions of 'initial segment': transitive subclass, transitive subclass that is closed under subsets and rank-initial segment. Paul Gorbow, in his Ph.D. thesis, systematically studies versions of H. Friedman's self-embedding that yield isomorphisms between a countable nonstandard model of set theory and a rank-initial segment of itself. In these two talks I will discuss recent joint work with Ali Enayat that investigates models of set theory that are isomorphic to a transitive subclass of itself. We call the maps witnessing these isomorphisms 'initial self-embeddings'. I will outline a proof of a refinement of H. Friedman's Theorem that guarantees the existence of initial self-embeddings for certain subsystems of ZF without the powerset axiom. I will then discuss several examples including a nonstandard model of ZFC minus the powerset axiom that admits no initial self-embedding, and models that separate the three different notions of self-embedding for models of set theory. Finally, I will discuss two interesting applications of our version of H. Freidman's Theorem. The first of these is a refinement of a result due to Quinsey that guarantees the existence of partially elementary proper transitive subclasses of non-standard models of ZF minus the powerset axiom. The second result shows that every countable model of ZF with a nonstandard natural number is isomorphic to a transitive subclass of the hereditarily countable sets of its own constructible universe.
- - - - Thursday, Jun 4, 2020 - - - -
- - - - Friday, Jun 5, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, June 5, 2pm
TBA
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)
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Set theory seminar this week: Michael Hrusak
Set theory seminar this week: Vinicius de Oliveira Rodrigues
Abstract: J. Ginsburg has asked what is the relation between the pseudocompactness of the-th power of a topological space
and the pseudocompactness of its Vietoris Hyperspace,
. M. Hrusak, I. Martínez-Ruiz and F. Hernandez-Hernandez studied this question restricted to Isbell-Mrówka spaces, that is, spaces of the form
where A is an almost disjoint family. Regarding these spaces, if
is pseudocompact, then
is also pseudocompact, and
is pseudocompact iff
is a MAD family. They showed that if the cardinal characteristic
is
, then for every MAD family
,
is pseudocompact, and if the cardinal characteristic
is less than
, there exists a MAD family
such that
is not pseudocompact. They asked if there exists a MAD family
(in ZFC) such that
is pseudocompact.
In this talk, we present some new results on the (consistent) existence of MAD families whose hyperspaces of their Isbell-Mrówka spaces are (or are not) pseudocompact by constructing new examples. Moreover, we give some combinatorial equivalences for every Isbell-Mrówka space from a MAD family having pseudocompact hyperspace. This is a joint work with, O. Guzman, M. Hrusak, S. Todorcevic and A. Tomita.
This Week in Logic at CUNY
- - - - Monday, May 18, 2020 - - - -
- - - - Tuesday, May 19, 2020 - - - -
- - - - Wednesday, May 20, 2020 - - - -
- - - - Thursday, May 21, 2020 - - - -
- - - - Friday, May 22, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, May 15, 2pm
Ali Enayat, University of Gothenburg
Recursively saturated models of set theory and their close relatives: Part II
A model M of set theory is said to be 'condensable' if there is an 'ordinal' α of M such that the rank initial segment of M determined by α is both isomorphic to M, and an elementary submodel of M for infinitary formulae appearing in the well-founded part of M. Clearly if M is condensable, then M is ill-founded. The work of Barwise and Schlipf in the mid 1970s showed that countable recursively saturated models of ZF are condensable.
In this two-part talk, we present a number of new results related to condensable models, including the following two theorems.
Theorem 1. Assuming that there is a well-founded model of ZFC plus 'there is an inaccessible cardinal', there is a condensable model M of ZFC which has the property that every definable element of M is in the well-founded part of M (in particular, M is ω-standard, and therefore not recursively saturated).
Theorem 2. The following are equivalent for an ill-founded model M of ZF of any cardinality:
(a) M is expandable to Gödel-Bernays class theory plus Δ11-Comprehension.
(b) There is a cofinal subset of 'ordinals' α of M such that the rank initial segment of M determined by α is an elementary submodel of M for infinitary formulae appearing in the well-founded part of M.
Moreover, if M is a countable ill-founded model of ZFC, then conditions (a) and (b) above are equivalent to:
(c) M is expandable to Gödel-Bernays class theory plus Δ11-Comprehension + Σ12-Choice.
- - - - Monday, May 25, 2020 - - - -
- - - - Tuesday, May 26, 2020 - - - -
- - - - Wednesday, May 27, 2020 - - - -
- - - - Thursday, May 28, 2020 - - - -
- - - - Friday, May 29, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, May 22, 2pm
TBA
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)
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This Week in Logic at CUNY
- - - - Monday, May 11, 2020 - - - -
- - - - Tuesday, May 12, 2020 - - - -
- - - - Wednesday, May 13, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, May 13
Bounded finite set theory
There is a well-known close logical connection between PA and finite set theory. Is there a set theory that corresponds in an analogous way to bounded arithmetic IΔ0? I propose a candidate for such a theory, called IΔ0S, and consider the questions: what set-theoretic axioms can it prove? And given a model M of IΔ0 is there a model of IΔ0S whose ordinals are isomorphic to M? The answer is yes if M is a model of Exp; to obtain the answer we use a new way of coding sets by numbers.
- - - - Thursday, May 14, 2020 - - - -
- - - - Friday, May 15, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, May 15, 2pm
Ali Enayat, University of Gothenburg
Recursively saturated models of set theory and their close relatives: Part I
A model M of set theory is said to be 'condensable' if there is an 'ordinal' α of M such that the rank initial segment of M determined by α is both isomorphic to M, and an elementary submodel of M for infinitary formulae appearing in the well-founded part of M. Clearly if M is condensable, then M is ill-founded. The work of Barwise and Schlipf in the mid 1970s showed that countable recursively saturated models of ZF are condensable.
In this two-part talk, we present a number of new results related to condensable models, including the following two theorems.
Theorem 1. Assuming that there is a well-founded model of ZFC plus 'there is an inaccessible cardinal', there is a condensable model M of ZFC which has the property that every definable element of M is in the well-founded part of M (in particular, M is ω-standard, and therefore not recursively saturated).
Theorem 2. The following are equivalent for an ill-founded model M of ZF of any cardinality:
(a) M is expandable to Gödel-Bernays class theory plus Δ11-Comprehension.
(b) There is a cofinal subset of 'ordinals' α of M such that the rank initial segment of M determined by α is an elementary submodel of M for infinitary formulae appearing in the well-founded part of M.
Moreover, if M is a countable ill-founded model of ZFC, then conditions (a) and (b) above are equivalent to:
(c) M is expandable to Gödel-Bernays class theory plus Δ11-Comprehension + Σ12-Choice.
- - - - Monday, May 18, 2020 - - - -
- - - - Tuesday, May 19, 2020 - - - -
- - - - Wednesday, May 20, 2020 - - - -
- - - - Thursday, May 21, 2020 - - - -
- - - - Friday, May 22, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, May 15, 2pm
Ali Enayat, University of Gothenburg
Recursively saturated models of set theory and their close relatives: Part II
A model M of set theory is said to be 'condensable' if there is an 'ordinal' α of M such that the rank initial segment of M determined by α is both isomorphic to M, and an elementary submodel of M for infinitary formulae appearing in the well-founded part of M. Clearly if M is condensable, then M is ill-founded. The work of Barwise and Schlipf in the mid 1970s showed that countable recursively saturated models of ZF are condensable.
In this two-part talk, we present a number of new results related to condensable models, including the following two theorems.
Theorem 1. Assuming that there is a well-founded model of ZFC plus 'there is an inaccessible cardinal', there is a condensable model M of ZFC which has the property that every definable element of M is in the well-founded part of M (in particular, M is ω-standard, and therefore not recursively saturated).
Theorem 2. The following are equivalent for an ill-founded model M of ZF of any cardinality:
(a) M is expandable to Gödel-Bernays class theory plus Δ11-Comprehension.
(b) There is a cofinal subset of 'ordinals' α of M such that the rank initial segment of M determined by α is an elementary submodel of M for infinitary formulae appearing in the well-founded part of M.
Moreover, if M is a countable ill-founded model of ZFC, then conditions (a) and (b) above are equivalent to:
(c) M is expandable to Gödel-Bernays class theory plus Δ11-Comprehension + Σ12-Choice.
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)
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Set theory seminar this Friday: Dima Sinapova
This Week in Logic at CUNY
I am starting the Oxford Set Theory Seminar, to be held online via Zoom for the foreseeable future. All set theorists are welcome to participate. You can find a schedule of this term's talks at http://jdh.hamkins.org/oxford-set-theory-seminar/ .
Jonas
- - - - Tuesday, May 5, 2020 - - - -
- - - - Wednesday, May 6, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, May 6, 7:00pm
May 6
Ali Enayat, University of Gothenburg
The Barwise-Schlipf characterization of recursive saturation of models of PA: Part II
The subject of this two-part talk is a 1975 Barwise-Schlipf landmark paper, whose main theorem asserts that a nonstandard model M of PA is recursively saturated iff M has an expansion to a model of the subsystem Δ11−CA0 of second order arithmetic. The impression one gets from reading the Barwise-Schlipf paper is that the left-to-right direction of the theorem is deep since it relies on sophisticated techniques from admissible set theory, and that the other direction is fairly routine.
As it turns out, the exact opposite is the case: the left-to-right direction of the Barwise-Schlipf theorem lends itself to a proof from first principles (as observed independently by Jonathan Stavi and Sol Feferman not long after the appearance of the Barwise-Schmerl paper); and moreover, as recently shown in my joint work with Jim Schmerl, there is a crucial error in the Barwise-Schlipf proof of the right-to-left direction of the theorem, an error that can be circumvented by a rather nontrivial argument. As I will explain, certain results from the joint work of Matt Kaufmann and Jim Schmerl in the mid-1980s on 'lofty' models of arithmetic come in handy for the analysis of the error, and for circumventing it.
In part I, after going over some history, and preliminaries, I will discuss (1) the gap in the Barwise-Schlipf paper, and (2) the aforementioned Feferman-Stavi proof. In part II, I will focus on how the gap can be circumvented with a proof strategy very different from that Barwise and Schlipf.
- - - - Thursday, May 7, 2020 - - - -
- - - - Friday, May 8, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, May 8, 2pm
TBA
Next Week in Logic at CUNY:
- - - - Monday, May 11, 2020 - - - -
- - - - Tuesday, May 12, 2020 - - - -
- - - - Wednesday, May 13, 2020 - - - -
- - - - Thursday, May 14, 2020 - - - -
- - - - Friday, May 15, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, May 15, 2pm
Ali Enayat, University of Gothenburg
Recursively saturated models of set theory and their close relatives: Part I
A model M of set theory is said to be 'condensable' if there is an 'ordinal' α of M such that the rank initial segment of M determined by α is both isomorphic to M, and an elementary submodel of M for infinitary formulae appearing in the well-founded part of M. Clearly if M is condensable, then M is ill-founded. The work of Barwise and Schlipf in the mid 1970s showed that countable recursively saturated models of ZF are condensable.
In this two-part talk, we present a number of new results related to condensable models, including the following two theorems.
Theorem 1. Assuming that there is a well-founded model of ZFC plus 'there is an inaccessible cardinal', there is a condensable model M of ZFC which has the property that every definable element of M is in the well-founded part of M (in particular, M is ω-standard, and therefore not recursively saturated).
Theorem 2. The following are equivalent for an ill-founded model M of ZF of any cardinality:
(a) M is expandable to Gödel-Bernays class theory plus Δ11-Comprehension.
(b) There is a cofinal subset of 'ordinals' α of M such that the rank initial segment of M determined by α is an elementary submodel of M for infinitary formulae appearing in the well-founded part of M.
Moreover, if M is a countable ill-founded model of ZFC, then conditions (a) and (b) above are equivalent to:
(c) M is expandable to Gödel-Bernays class theory plus Δ11-Comprehension + Σ12-Choice.
- - - - Other Logic News - - - -
See schedule at:
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
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Wednesday seminar
Set theory seminar this week: Paul Szeptycki
This Week in Logic at CUNY
- - - - Tuesday, Apr 28, 2020 - - - -
- - - - Wednesday, Apr 29, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, April 29, 7:00pm
April 29
Ali Enayat, University of Gothenburg
The Barwise-Schlipf characterization of recursive saturation of models of PA
The subject of this talk is a 1975 Barwise-Schlipf landmark paper, whose main theorem asserts that a nonstandard model M of PA is recursively saturated iff M has an expansion to a model of the subsystem Δ11−CA0 of second order arithmetic. The impression one gets from reading the Barwise-Schlipf paper is that the left-to-right direction of the theorem is deep since it relies on sophisticated techniques from admissible set theory, and that the other direction is fairly routine.
As it turns out, the exact opposite is the case: the left-to-right direction of the Barwise-Schlipf theorem lends itself to a proof from first principles (as observed independently by Jonathan Stavi and Sol Feferman not long after the appearance of the Barwise-Schmerl paper); and moreover, as recently shown in my joint work with Jim Schmerl, there is a crucial error in the Barwise-Schlipf proof of the right-to-left direction of the theorem, an error that can be circumvented by a rather nontrivial argument. As I will explain, certain results from the joint work of Matt Kaufmann and Jim Schmerl in the mid-1980s on 'lofty' models of arithmetic come in handy for the analysis of the error, and for circumventing it.
- - - - Thursday, Apr 30, 2020 - - - -
- - - - Friday, May 1, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, May 1, 2pm
Joan Bagaria Universitat de Barcelona
TBA
Next Week in Logic at CUNY:
- - - - Monday, May 4, 2020 - - - -
- - - - Tuesday, May 5, 2020 - - - -
- - - - Wednesday, May 6, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, May 6, 7:00pm
May 6
Ali Enayat, University of Gothenburg
The Barwise-Schlipf characterization of recursive saturation of models of PA, part 2
The subject of this talk is a 1975 Barwise-Schlipf landmark paper, whose main theorem asserts that a nonstandard model M of PA is recursively saturated iff M has an expansion to a model of the subsystem Δ11−CA0 of second order arithmetic. The impression one gets from reading the Barwise-Schlipf paper is that the left-to-right direction of the theorem is deep since it relies on sophisticated techniques from admissible set theory, and that the other direction is fairly routine.
As it turns out, the exact opposite is the case: the left-to-right direction of the Barwise-Schlipf theorem lends itself to a proof from first principles (as observed independently by Jonathan Stavi and Sol Feferman not long after the appearance of the Barwise-Schmerl paper); and moreover, as recently shown in my joint work with Jim Schmerl, there is a crucial error in the Barwise-Schlipf proof of the right-to-left direction of the theorem, an error that can be circumvented by a rather nontrivial argument. As I will explain, certain results from the joint work of Matt Kaufmann and Jim Schmerl in the mid-1980s on 'lofty' models of arithmetic come in handy for the analysis of the error, and for circumventing it.
- - - - Thursday, May 7, 2020 - - - -
- - - - Friday, May 8, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, May 8, 2pm
TBA
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
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Wednesday seminar
Wednesday seminar
Set theory seminar this week: Todd Eisworth
This Week in Logic at CUNY
- - - - Monday, Apr 20, 2020 - - - -
- - - - Tuesday, Apr 21, 2020 - - - -
- - - - Wednesday, Apr 22, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, April 22, 7:00pm
Recall that given a complete theory T and a type p(x) the Hanf number for p(x) is the least cardinal κ so that any model of T of size κ realizes p(x) (if such a κ exists and ∞ otherwise). The Hanf number for T, denoted H(T), is the supremum of the successors of the Hanf numbers for all possible types p(x) whose Hanf numbers are <∞. We have seen so far in the seminar that for any complete, consistent T in a countable language H(T)≤ℶω1 (a result due to Morley). In this talk I will present the following theorems: (1) The Hanf number for true arithmetic is ℶω (Abrahamson-Harrington-Knight) but (2) the Hanf number for False Arithmetic is ℶω1 (Abrahamson-Harrington)
- - - - Thursday, Apr 23, 2020 - - - -
- - - - Friday, Apr 24, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, April 24, 2pm
- - - - Monday, Apr 27, 2020 - - - -
- - - - Tuesday, Apr 28, 2020 - - - -
- - - - Wednesday, Apr 29, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, April 29, 7:00pm
April 29
Ali Enayat, University of Gothenburg
The Barwise-Schlipf characterization of recursive saturation of models of PA
The subject of this talk is a 1975 Barwise-Schlipf landmark paper, whose main theorem asserts that a nonstandard model M of PA is recursively saturated iff M has an expansion to a model of the subsystem Δ11−CA0 of second order arithmetic. The impression one gets from reading the Barwise-Schlipf paper is that the left-to-right direction of the theorem is deep since it relies on sophisticated techniques from admissible set theory, and that the other direction is fairly routine.
As it turns out, the exact opposite is the case: the left-to-right direction of the Barwise-Schlipf theorem lends itself to a proof from first principles (as observed independently by Jonathan Stavi and Sol Feferman not long after the appearance of the Barwise-Schmerl paper); and moreover, as recently shown in my joint work with Jim Schmerl, there is a crucial error in the Barwise-Schlipf proof of the right-to-left direction of the theorem, an error that can be circumvented by a rather nontrivial argument. As I will explain, certain results from the joint work of Matt Kaufmann and Jim Schmerl in the mid-1980s on 'lofty' models of arithmetic come in handy for the analysis of the error, and for circumventing it.
- - - - Thursday, Apr 30, 2020 - - - -
- - - - Friday, May 1, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, May 1, 2pm
Joan Bagaria Universitat de Barcelona
TBA
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
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Wednesday seminar
Wednesday seminar
Set theory seminar this week: Matteo Viale
Abstract: We show that (assuming large cardinals) set theory is a tractable (and we dare to say tame) first order theory when formalized in a first order signature with natural predicate symbols for the basic definable concepts of second and third order arithmetic, and appealing to the model-theoretic notions of model completeness and model companionship.
Specifically we develop a general framework linking generic absoluteness results to model companionship and show that (with the required care in details) a-property formalized in an appropriate language for second or third order number theory is forcible from some T extending ZFC + large cardinals if and only if it is consistent with the universal fragment of T if and only if it is realized in the model companion of T.
Part (but not all) of our results are conditional to the proof of Schindler and Asperò that Woodin’s axiom (*) can be forced by a stationary set preserving forcing.
This Week in Logic at CUNY
- - - - Monday, Apr 13, 2020 - - - -
- - - - Tuesday, Apr 14, 2020 - - - -
- - - - Wednesday, Apr 15, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center
Wednesday, April 15, 7:00pm
Non-standard models of arithmetic and their standard systems
- - - - Thursday, Apr 16, 2020 - - - -
- - - - Friday, Apr 17, 2020 - - - -
Set Theory Seminar
CUNY Graduate Center
Friday, April 17, 2pm
Corey Switzer, CUNY
Specializing Wide Trees Without Adding Reals
Next Week in Logic at CUNY:
- - - - Monday, Apr 20, 2020 - - - -
- - - - Tuesday, Apr 21, 2020 - - - -
- - - - Wednesday, Apr 22, 2020 - - - -
- - - - Thursday, Apr 23, 2020 - - - -
- - - - Friday, Apr 24, 2020 - - - -
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
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Set theory seminar this week: Keegan Dasilva Barbosa
Abstract: We will prove that under the proper forcing axiom, the class of all Aronszajn lines behave like-scattered orders under the embeddability relation. In particular, we show that the class of better quasi order labeled fragmented Aronszajn lines is itself a better quasi order. Moreover, we show that every better quasi order labeled Aronszajn line can be expressed as a finite sum of labeled types which are algebraically indecomposable. By encoding lines with finite labeled trees, we are also able to deduce a decomposition result, that for every Aronszajn line
, there is an
such that for any finite colouring of
, there is a subset
of
isomorphic to
which uses no more than
colours.
Time: Apr 10, 2020 01:30 PM Eastern Time (US and Canada)
Logic Seminar Wed 8 April 2020 17:00 hrs at NUS via Zoom
Set theory seminar this Friday: Iván Ongay Valverde
Abstract: In 1993, Newelski and Roslanowski studied some cardinal characteristics related to the unsymmetric game (I, as Geschke, called them the localization numbers). While doing this, they found the n-localization property. When a forcing has this property, you can ensure that all new reals are 'tame' somehow (for example, you do not add Cohen or Random reals).In a different line of study, Andreas Blass worked with some cardinal characteristics related to the idea of guessing correctly a real number given certain amount of information (he called them evasion and prediction numbers). In 2010, it was an open question whether some possible variations of these numbers were known cardinal characteristics or not.Impressively, these two notions are related.In this talk, we will show that the k global adaptive prediction numbers are not any other cardinal characteristic. In particular, they are not the localization numbers. To do this, we will use techniques analogue to Newelski and Roslanowski and we will show that the n-localization can be weakened to get their result.
Topic: Set Theory Seminar
Join Zoom Meeting
https://yorku.zoom.us/j/925557716
Meeting ID: 925 557 716
Zoom Address for the Seminar Talk Next Week Wednesday (Logic Seminar NUS)
Zoom Address for the Seminar Talk Next Week Wednesday (Logic Seminar NUS)
Logic Seminar Talk 1 April 2020 17:00 hrs at NUS
Wednesday seminar
Wednesday seminar
Set Theory Seminar this week: Ming Xiao (important meeting information inside!)
Wednesday seminar
Logic Seminar 18 March 2020 17:00 hrs at NUS
This Week in Logic at CUNY
Set theory seminar this Friday: Jeffrey Bergfalk
2. It yields refinements of classical homological and cohomological invariants which are valuable in their own right for the study of topological spaces.
We term the framework of these refined invariants definable (co)homology; this framework amounts to a retention of the descriptive set-theoretic information inhering in algebraic topology computations. These invariants are strong enough to imply several topological rigidity results concerning solenoids (of any dimension) and maps thereon. We will also show that techniques from algebraic topology can, reciprocally, extend the reach of descriptive set theory, by bounding, and in some cases precisely determining, the Borel complexity of classification problems concerning C*- algebras, their automorphisms, or Hermitian line bundles.
This Week in Logic at CUNY
Logic and Metaphysics Workshop
Date: Monday, March 9, 4.15-6.15
Place: Room 7395, CUNY Graduate Center
Antonella Mallozzi (Providence College).
Title: Is There an Absolute Modality?
Abstract: Modality seems distinctively pluralistic: there are many kinds of possibility and necessity (logical, physical, metaphysical, normative, etc.), which seem significantly different from one another. However, the various modalities also seem to have much in common–perhaps simply in virtue of being kinds of modality. Should we suppose that there is some fundamental modality, one to which all the other modalities can be somehow reduced? Modal Monism says yes. Particularly, monists may treat the different modalities as relative to some absolute modality. However, Monism, reductionism, and absolute modality need not be a package. Specifically, the claim that some modality is absolute can be understood in ways which are independent of Monism and reductionism. In this talk, I raise concerns for monistic and reductionist programs in modal metaphysics, while also arguing that the notion of absolute modality is ambiguous. Depending on the framework, it means different things and captures quite different desiderata. After exploring several ways of disambiguating it, I suggest that while we possess and deploy a concept of absolute modality, that may be empty; or, otherwise put, no modal truth has the property of being “absolute”. I propose a pluralistic picture that still treats the different modalities as relative, while avoiding both absolute modality and reductionism. Importantly, the proposal won’t impact the philosophical significance of metaphysical modality.
- - - - Tuesday, Mar 10, 2020 - - - -
- - - - Wednesday, Mar 11, 2020 - - - -
The New York City Category Theory Seminar
Department of Computer Science, Department of Mathematics
The Graduate Center of The City University of New York
Date and Time: Wednesday March 11, 2020, 7:00 - 8:30 PM., Room 6417.
Title: Modeling Probability Distributions as Quantum States.
Abstract: This talk features a passage from classical probability to quantum probability. The quantum version of a classical probability distribution is a density operator on a Hilbert space. The quantum version of a marginal probability distribution is a reduced density operator, and the operation that plays the role of marginalization is the partial trace. In particular, every joint probability distribution on a finite set can be modeling as a rank 1 density operator—a pure quantum state. With the partial trace, we recover the classical marginal probabilities, but we also uncover additional information. This extra information can be understood explicitly from the spectral information of the reduced density operators. I’ll describe these ideas and share how they contribute to understanding mathematical structure within natural language.
- - - - Thursday, Mar 12, 2020 - - - -
- - - - Friday, Mar 13, 2020 - - - -
CUNY Graduate Center, Room 6417
Friday, March 13, 12:30-2:00pm
TBA
CUNY Graduate Center, Room 6417
Friday, March 13, 2:00-3:30pm
The complexity of radical constructions in rings and modules
We present two different elementary algebraic constructions that are as complicated as possible and whose complexity vastly exceeds those typically found in the elementary algebra literature. The first is the prime radical of a noncommutative ring, while the second is the radical of a module. These constructions contrast similar constructions in more familiar contexts that we will also mention along the way. We will spend most of our time describing how to construct radicals that are as complicated as possible from a computability point of view.
- - - - Monday, Mar 16, 2020 - - - -
Logic and Metaphysics Workshop
Date: Monday, March 16, 4.15-6.15
Place: Room 7395, CUNY Graduate Center
Title: The Statistical Nature of Causation
Abstract: For over a hundred years econometricians, epidemiologists, educational sociologists and other non-experimental scientists have used asymmetric correlational patterns to infer directed causal structures. It is odd, to say the least, that no philosophical theories of causation cast any light on why these techniques work. Why do the directed causal structures line up with the asymmetric correlational patterns? Judea Pearl says that the correspondence is a “gift from the gods”. Metaphysics owes us a better answer. I shall attempt to sketch the outline of one.
- - - - Tuesday, Mar 17, 2020 - - - -
- - - - Wednesday, Mar 18, 2020 - - - -
- - - - Thursday, Mar 19, 2020 - - - -
- - - - Friday, Mar 20, 2020 - - - -
When? Friday March 20, Noon-5pm
Where? CUNY Graduate Center, room TBA
Who?
Will Nava, NYU, ‘Expressability and the (Un)Paradoxicality Paradoxes’
Brian Porter, GC, ‘Paraconsistent and Paracomplete Solutions to the Validity Curry Paradox’
Chris Scambler, NYU, ‘Metainferences and Paradox’
Open to? All interested
Queries? Graham Priest, priest.graham@gmail.com
The workshop is sponsored by the Kripke Center.
- - - - Other Logic News - - - -
This is a three day conference (April 22-24) in the mathematical field of set theory to be held at the CUNY Graduate Center. Consult the website (https://nylogic.github.io/MAMLSSpringFling/home.html) for more details.
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Logic Seminar Wed 11 March 2020 17:00 hrs at NUS by Thilo Weinert
Fulgencio Lopez, Uncountable equilateral sets and anti-Ramsey families of functions.
Set theory seminar this Friday
This Week in Logic at CUNY
- - - - Monday, Mar 2, 2020 - - - -
Logic and Metaphysics Workshop
Date: Monday, March 2, 4.15-6.15
Place: Room 7395, CUNY Graduate Center
Title: Deductive Systems with Unified Multiple-Conclusion Rules
Abstract: Some people fight for the rights of animals, I am fighting for the rights of rejected propositions. Following the approach suggested by Brentano and accepted and developed by Lukasiewicz, I study the deductive systems that treat asserted and rejected propositions equally, in the same way. By “statement,” we understand the expressions of form +A – “A being asserted”, and -A$ – “A being rejected”, where A is a proposition. Accordingly, by a “unified logic,” we understand a consequence relation between sets of statements and statements. We introduce the unified deductive systems which can be used to define the unified logics. Unified deductive system consists of axioms, anti-axioms, and the multiple conclusion inference rules which premises and conclusions are the statements rather than the propositions. In particular, we study the deductive systems that contain the coherency rule, which means that one cannot assert and reject the same proposition at the same time, and the fullness rule, which means that each proposition is either asserted or rejected. Inclusion of these rules though does not enforce the law of excluded middle, or the law of non-contradiction on the propositional level.
- - - - Tuesday, Mar 3, 2020 - - - -
- - - - Wednesday, Mar 4, 2020 - - - -
Department of Computer Science, Department of Mathematics
The Graduate Center of The City University of New York
Date and Time: Wednesday March 4, 2020, 7:00 - 8:30 PM., Room 6417.
Title: Hierarchy and Anisotropy in Categorical Ontology.
Abstract: The theory of sheaves on a site allows us to break down objects into local pieces and recover data about the global object. We wish to treat systems outside of mathematics in the same way: by breaking down objects into local pieces, analyzing the local pieces, and recombining to get an analysis of the whole. When running a simulation, it's not always relevant to understand the atoms of every object, sometimes it is enough to understand objects abstractly, this is the concept of "anisotropy". We propose a modeling scheme that follows the development of sheaf theory, and adds a notion of hierarchical anisotropy. Namely, instead of a covering in a site, {U_i -> X}, we will treat the U_i and X in two different categories, with "Ontological Expansions" O(X) = {U_i}. In this way, we can decide to treat objects globally, or if we need more specific information, we can expand into local pieces. To this end we define a Hierarchical Ontology.
- - - - Thursday, Mar 5, 2020 - - - -
- - - - Friday, Mar 6, 2020 - - - -
Model Theory Seminar
CUNY Graduate Center, Room 6417
Friday, March 6, 12:30-2:00pm
Computability of the countable saturated differentially closed field
CUNY Graduate Center, Room 6417
Friday, March 6, 2:00-3:30pm
Johanna Franklin, Hofstra University
Lowness for isomorphism and Turing degrees
A Turing degree is low for isomorphism if whenever it can compute an isomorphism between two countably presented structures, there is already a computable isomorphism between them and thus there is no need to use the degree as an oracle at all. I will discuss the types of degrees that are low for isomorphism and the extent to which this class of degrees has the same properties as other lowness classes.
This work is joint with Reed Solomon.
Next Week in Logic at CUNY:
- - - - Monday, Mar 9, 2020 - - - -
Logic and Metaphysics Workshop
Date: Monday, March 9, 4.15-6.15
Place: Room 7395, CUNY Graduate Center
Alex Citkin (Metropolitan Telecommunications).
Title: Deductive Systems with Unified Multiple-Conclusion Rules
Abstract: Some people fight for the rights of animals, I am fighting for the rights of rejected propositions. Following the approach suggested by Brentano and accepted and developed by Lukasiewicz, I study the deductive systems that treat asserted and rejected propositions equally, in the same way. By “statement,” we understand the expressions of form +A – “A being asserted”, and -A$ – “A being rejected”, where A is a proposition. Accordingly, by a “unified logic,” we understand a consequence relation between sets of statements and statements. We introduce the unified deductive systems which can be used to define the unified logics. Unified deductive system consists of axioms, anti-axioms, and the multiple conclusion inference rules which premises and conclusions are the statements rather than the propositions. In particular, we study the deductive systems that contain the coherency rule, which means that one cannot assert and reject the same proposition at the same time, and the fullness rule, which means that each proposition is either asserted or rejected. Inclusion of these rules though does not enforce the law of excluded middle, or the law of non-contradiction on the propositional level.
- - - - Tuesday, Mar 10, 2020 - - - -
- - - - Wednesday, Mar 11, 2020 - - - -
The New York City Category Theory Seminar
Department of Computer Science, Department of Mathematics
The Graduate Center of The City University of New York
Date and Time: Wednesday March 11, 2020, 7:00 - 8:30 PM., Room 6417.
Title: Modeling Probability Distributions as Quantum States.
Abstract: This talk features a passage from classical probability to quantum probability. The quantum version of a classical probability distribution is a density operator on a Hilbert space. The quantum version of a marginal probability distribution is a reduced density operator, and the operation that plays the role of marginalization is the partial trace. In particular, every joint probability distribution on a finite set can be modeling as a rank 1 density operator—a pure quantum state. With the partial trace, we recover the classical marginal probabilities, but we also uncover additional information. This extra information can be understood explicitly from the spectral information of the reduced density operators. I’ll describe these ideas and share how they contribute to understanding mathematical structure within natural language.
- - - - Thursday, Mar 12, 2020 - - - -
- - - - Friday, Mar 13, 2020 - - - -
CUNY Graduate Center, Room 6417
Friday, March 13, 2:00-3:30pm
TBA
- - - - Other Logic News - - - -
BEST is an international conference featuring talks on a broad range of recent advances in research in set theory, logic, and related fields. Researchers from all areas of set theory and logic are welcome. BEST particularly aims to support the careers of young researchers. The conference is organized by the Set Theory and Logic group at Boise State University and is structured as a symposium of the annual meeting of the AAAS, Pacific Division.
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Wednesday seminar
Tomasz Kochanek, On representations of the Calkin algebra - the noncommutative analogue of P(N)/Fin or l∞/c0 II
(KGRC) research seminar talk on Thursday, March 5
Set Theory Seminar this Friday
Hi everyone,I will talk this week about selectivity properties of spaces.Abstract: This talk addresses several questions of Feng, Gruenhage, and Shen which arose from Michael's theory of continuous selections from countable spaces. This theory is concerned with the following general question about topological spaces: when does a map frominto the hyperspace of closed nonempty subsets of
admit a continuous selection
?
We construct a space which is-selective but not
-selective from
, and an
-selective space which is not selective for a
-point ultrafilter from CH. We also produce ZFC examples of Fréchet spaces where countable subsets are first countable which are not
-selective. All of the notions will be defined in the talk, joint work with Paul Szeptycki.
The talk will be held at the usual time and place on Friday, February 14 in Fields 210 from 1:30 to 3:00. If you will attend the talk, please register using the following link:Thanks,Bill Chen
Fernando Javier Núñez Rosales: Teoría descriptiva de grupos polacos no arquimedianos de transformaciones
Logic Seminar 4 March 2020 17:00 hrs at NUS by Andre Nies
SPECIAL ANNOUNCEMENT - This Week in Logic at CUNY - Two add'l talks today
Hi everyone,
Please see the announcement below, provided by Dennis Sullivan.
Best,
Jonas
---------------------------------
Prof. Francisco Javier Torres de Lizaur from Spain will give two talks today at the Einstein Chair seminar today, February 24, 2020:
The first will relate to geometry.
The second will relate to 3D fluid solutions in space to logic, computer science and PDE.
Namely, at 4:00p in logic knowing if a point enters a region contains the halting problem.
This affects PDE, analysis and computer science and at 2:00p finding links knots and foliations in stationary solutions of Euler’s fluid PDE in 3D.
<2:00p to tea then 4:00 to 5:00p>
<ROOM 6417>
This Week in Logic at CUNY
Logic and Metaphysics Workshop
Date: Monday, February 24, 4.15-6.15
Place: Room 7395, CUNY Graduate Center
Dongwoo Kim (CUNY)
Title: A Truthmaker Semantics for Modal Logics
Abstract: This paper attempts to provide an exact truthmaker semantics for a family of normal modal propositional logic. The new semantics can be regarded as an “exactification” of the Kripke semantics in the sense of Fine (2014). For it offers an account of the accessibility relation on worlds in terms of the banning and allowing relations on states. The main idea is that an exact truthmaker for “Necessarily P” is a state that bans the exact falsifiers of P from obtaining, and an exact truthmaker for “Possibly P” is a state that allows the exact verifiers of P to obtain.
- - - - Tuesday, Feb 25, 2020 - - - -
- - - - Wednesday, Feb 26, 2020 - - - -
The New York City Category Theory Seminar
Department of Computer Science, Department of Mathematics
The Graduate Center of The City University of New York
Speaker: Noson S. Yanofsky, Brooklyn College, CUNY.
Date and Time: Wednesday February 26, 2020, 7:00 - 8:30 PM., Room 6417.
Abstract: We will be talking about Polynomial categories and Kleisli categories of cotriples. We will also talk about coproducts in Cartesian closed categories and natural number objects.
- - - - Thursday, Feb 27, 2020 - - - -
- - - - Friday, Feb 28, 2020 - - - -
CUNY Graduate Center, Room 6417
Friday, February 28, 2:00-3:30pm
TBA
Next Week in Logic at CUNY:
- - - - Monday, Mar 2, 2020 - - - -
Logic and Metaphysics Workshop
Date: Monday, March 2, 4.15-6.15
Place: Room 7395, CUNY Graduate Center
Title: Deductive Systems with Unified Multiple-Conclusion Rules
Abstract: Some people fight for the rights of animals, I am fighting for the rights of rejected propositions. Following the approach suggested by Brentano and accepted and developed by Lukasiewicz, I study the deductive systems that treat asserted and rejected propositions equally, in the same way. By “statement,” we understand the expressions of form +A – “A being asserted”, and -A$ – “A being rejected”, where A is a proposition. Accordingly, by a “unified logic,” we understand a consequence relation between sets of statements and statements. We introduce the unified deductive systems which can be used to define the unified logics. Unified deductive system consists of axioms, anti-axioms, and the multiple conclusion inference rules which premises and conclusions are the statements rather than the propositions. In particular, we study the deductive systems that contain the coherency rule, which means that one cannot assert and reject the same proposition at the same time, and the fullness rule, which means that each proposition is either asserted or rejected. Inclusion of these rules though does not enforce the law of excluded middle, or the law of non-contradiction on the propositional level.
- - - - Tuesday, Mar 3, 2020 - - - -
- - - - Wednesday, Mar 4, 2020 - - - -
Department of Computer Science, Department of Mathematics
The Graduate Center of The City University of New York
Date and Time: Wednesday March 4, 2020, 7:00 - 8:30 PM., Room 6417.
Title: Hierarchy and Anisotropy in Categorical Ontology.
Abstract: The theory of sheaves on a site allows us to break down objects into local pieces and recover data about the global object. We wish to treat systems outside of mathematics in the same way: by breaking down objects into local pieces, analyzing the local pieces, and recombining to get an analysis of the whole. When running a simulation, it's not always relevant to understand the atoms of every object, sometimes it is enough to understand objects abstractly, this is the concept of "anisotropy". We propose a modeling scheme that follows the development of sheaf theory, and adds a notion of hierarchical anisotropy. Namely, instead of a covering in a site, {U_i -> X}, we will treat the U_i and X in two different categories, with "Ontological Expansions" O(X) = {U_i}. In this way, we can decide to treat objects globally, or if we need more specific information, we can expand into local pieces. To this end we define a Hierarchical Ontology.
- - - - Thursday, Mar 5, 2020 - - - -
- - - - Friday, Mar 6, 2020 - - - -
Logic Workshop
CUNY Graduate Center, Room 6417
Friday, March 6, 2:00-3:30pm
Johanna Franklin, Hofstra University
Lowness for isomorphism and Turing degrees
A Turing degree is low for isomorphism if whenever it can compute an isomorphism between two countably presented structures, there is already a computable isomorphism between them and thus there is no need to use the degree as an oracle at all. I will discuss the types of degrees that are low for isomorphism and the extent to which this class of degrees has the same properties as other lowness classes.
This work is joint with Reed Solomon.
- - - - Other Logic News - - - -
BEST is an international conference featuring talks on a broad range of recent advances in research in set theory, logic, and related fields. Researchers from all areas of set theory and logic are welcome. BEST particularly aims to support the careers of young researchers. The conference is organized by the Set Theory and Logic group at Boise State University and is structured as a symposium of the annual meeting of the AAAS, Pacific Division.
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Tomasz Kochanek, On representations of the Calkin algebra - the noncommutative analogue of P(N)/Fin or l∞/c0
Wednesday seminar
This Week in Logic at CUNY
- - - - Monday, Feb 17, 2020 - - - -
- - - - Tuesday, Feb 18, 2020 - - - -
- - - - Wednesday, Feb 19, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center, Room 4213.03 (Math Thesis Room)
Wednesday, February 19, 6:30-8:00pm
James Geiser
Soundness and the Gödel Undecidability Theorem
The goal of Gödel’s argument that the theory (T) of Peano Arithmetic is not complete, was to show that the Gödel sentences, G , and it’s negation, are not provable in T, unless T is inconsistent. In this paper we examine the first half of this argument, namely, that from a hypothetical derivation, PG, of G, a derivation, Pf, can be constructed that ends in a contradiction. We make the observation that the Gödel argument depends on the metatheory concept of representability that, in turn, depends on the metatheory concept of soundness. Our analysis leads to two main observations, the first well know, and the second, a challenge to the standard undecidability argument.
1 – The existence of PG implies that T is unsound. This conclusion does not require the further construction, from PG, of the derivation Pf.
2 - We argue that effectuation of the construction of Pf is obstructed, because that effectuation requires acceptance of a contradiction in the metatheory regarding the soundness of T.
This is joint work with Catherine Hennix.
Department of Computer Science, Department of Mathematics
The Graduate Center of The City University of New York
Date and Time: Wednesday February 19, 2020, 7:00 - 8:30 PM., Room 6417.
Speaker: Todd Trimble, Western Connecticut State University.
Title: The Universal Property of the Bar Construction.
Abstract: The bar construction is a fundamental construction used throughout homological algebra and algebraic topology, including for example the construction of classifying bundles, deloopings of suitable H-spaces, and free resolutions of general algebras and the cohomology thereof. The underlying theme is that the bar construction produces canonical contractible or acyclic simplicial algebras, as usually explained by the acyclic models theorem. In this talk we sharpen this result, giving a precise sense in which the bar construction is a universal acyclic simplicial algebra, here recasting "acyclic" not as a property but as an algebraic structure, whereby acyclic structures are coalgebras over the decalage comonad.
- - - - Thursday, Feb 20, 2020 - - - -
- - - - Friday, Feb 21, 2020 - - - -
Logic Workshop
CUNY Graduate Center, Room 6417
Friday, February 21, 2:00-3:30pm
Andrey Morozov, Novosibirsk State University
On Σ-preorderings in HF(R)
We prove that ω1 cannot be embedded into any preordering Σ-definable with parameters in the hereditarily finite superstructure over the ordered field of real numbers, HF(R). As corollaries, we obtain characterizations of Σ-presentable ordinals and Gödel constructive sets of kind Lα. It also follows that there are no Σ-presentations for structures of T-, m-, 1-, and tt-degrees over HF(R).
- - - - Monday, Feb 24, 2020 - - - -
Logic and Metaphysics Workshop
Date: Monday, February 24, 4.15-6.15
Place: Room 7395, CUNY Graduate Center
Dongwoo Kim (CUNY)
Title: A Truthmaker Semantics for Modal Logics
Abstract: This paper attempts to provide an exact truthmaker semantics for a family of normal modal propositional logic. The new semantics can be regarded as an “exactification” of the Kripke semantics in the sense of Fine (2014). For it offers an account of the accessibility relation on worlds in terms of the banning and allowing relations on states. The main idea is that an exact truthmaker for “Necessarily P” is a state that bans the exact falsifiers of P from obtaining, and an exact truthmaker for “Possibly P” is a state that allows the exact verifiers of P to obtain.
- - - - Tuesday, Feb 25, 2020 - - - -
- - - - Wednesday, Feb 26, 2020 - - - -
The New York City Category Theory Seminar
Department of Computer Science, Department of Mathematics
The Graduate Center of The City University of New York
Date and Time: Wednesday February 26, 2020, 7:00 - 8:30 PM., Room 6417.
Abstract: We will be talking about Polynomial categories and Kleisli categories of cotriples. We will also talk about coproducts in Cartesian closed categories and natural number objects.
- - - - Thursday, Feb 27, 2020 - - - -
- - - - Friday, Feb 28, 2020 - - - -
CUNY Graduate Center, Room 6417
Friday, February 28, 2:00-3:30pm
TBA
- - - - Other Logic News - - - -
BEST is an international conference featuring talks on a broad range of recent advances in research in set theory, logic, and related fields. Researchers from all areas of set theory and logic are welcome. BEST particularly aims to support the careers of young researchers. The conference is organized by the Set Theory and Logic group at Boise State University and is structured as a symposium of the annual meeting of the AAAS, Pacific Division.
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Logic seminar this week cancelled
Wednesday seminar
Logic Seminar 19 Feb 2020 17:00 hrs at NUS
Set Theory Seminar this Friday
Boise Extravaganza in Set Theory, Ashland, OR, June 17-18, 2020
Ultrafilters and Ultraproducts Across Mathematics, Pisa, Italy, May 31-June 6, 2020
Logic Colloquium, Poznań, Poladn, July 13-18, 2020
This Week in Logic at CUNY
Logic and Metaphysics Workshop
Date: Monday, February 10, 4.15-6.15
Place: Room 7395, CUNY Graduate Center
Melissa Fusco (Columbia)
Is Free Choice Cancellable?
I explore the implications of the Tense Phrase deletion operation known as sluicing (Ross 1969) for the semantic and pragmatic literature on the Free Choice effect (Kamp 1973, von Wright 1969). I argue that the time-honored ‘I don’t know which’-riders on Free Choice sentences, traditionally taken to show that the effect is pragmatic, are sensitive to scope. Careful attention to such riders suggests that these sluices do not show cancellation on Free Choice antecedents in which disjunction scopes narrower than the modal.
- - - - Tuesday, Feb 11, 2020 - - - -
- - - - Wednesday, Feb 12, 2020 - - - -
NO TALKS TODAY - LINCOLN'S BIRTHDAY
- - - - Thursday, Feb 13, 2020 - - - -
- - - - Friday, Feb 14, 2020 - - - -
Logic Workshop
CUNY Graduate Center, Room 6417
Friday, February 14, 2:00-3:30pm
Bartosz Wcisło, University of Warsaw
Tarski boundary
Our talk concerns axiomatic theories of truth predicates. They are theories obtained by adding to Peano Arithmetic (PA) a fresh predicate T(x) with the intended reading 'x is (a code of) a true sentence in the language of arithmetic' together with some axioms governing newly added predicate.
The canonical example of such a theory is CT− (Compositional Truth). Its axioms state that the truth predicate is compositional. For instance, a conjunction is true iff both conjuncts are. If we add to CT− full induction in the extended language, we call the resulting theory CT.
It is easy to check that CT is not conservative over PA, i.e., it proves new arithmetical sentences. On the other hand, by a nontrivial theorem of Kotlarski, Krajewski, and Lachlan, CT− extends PA conservatively.
In our talk, we will discuss results on the strength of theories between CT− and CT. It turns out that the natural axioms concerning purely truth theoretic properties of the newly added predicate (as opposed to axiom schemes which are consequences of induction in more general context) are typically either conservative or exactly equal to CT0, the theory of compositional truth with Δ0-induction. Thus CT0 turns out to be a surprisingly robust theory and, arguably, the minimal 'natural' non-conservative theory of truth.
- - - - Monday, Feb 17, 2020 - - - -
- - - - Tuesday, Feb 18, 2020 - - - -
- - - - Wednesday, Feb 19, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center, Room 4213.03 (Math Thesis Room)
Wednesday, February 19, 6:30-8:00pm
James Geiser
Soundness and the Gödel Undecidability Theorem
The goal of Gödel’s argument that the theory (T) of Peano Arithmetic is not complete, was to show that the Gödel sentences, G , and it’s negation, are not provable in T, unless T is inconsistent. In this paper we examine the first half of this argument, namely, that from a hypothetical derivation, PG, of G, a derivation, Pf, can be constructed that ends in a contradiction. We make the observation that the Gödel argument depends on the metatheory concept of representability that, in turn, depends on the metatheory concept of soundness. Our analysis leads to two main observations, the first well know, and the second, a challenge to the standard undecidability argument.
1 – The existence of PG implies that T is unsound. This conclusion does not require the further construction, from PG, of the derivation Pf.
2 - We argue that effectuation of the construction of Pf is obstructed, because that effectuation requires acceptance of a contradiction in the metatheory regarding the soundness of T.
This is joint work with Catherine Hennix.
Department of Computer Science, Department of Mathematics
The Graduate Center of The City University of New York
Date and Time: Wednesday February 19, 2020, 7:00 - 8:30 PM., Room 6417.
Speaker: Todd Trimble, Western Connecticut State University.
Title: The Universal Property of the Bar Construction.
Abstract: The bar construction is a fundamental construction used throughout homological algebra and algebraic topology, including for example the construction of classifying bundles, deloopings of suitable H-spaces, and free resolutions of general algebras and the cohomology thereof. The underlying theme is that the bar construction produces canonical contractible or acyclic simplicial algebras, as usually explained by the acyclic models theorem. In this talk we sharpen this result, giving a precise sense in which the bar construction is a universal acyclic simplicial algebra, here recasting "acyclic" not as a property but as an algebraic structure, whereby acyclic structures are coalgebras over the decalage comonad.
- - - - Thursday, Feb 20, 2020 - - - -
- - - - Friday, Feb 21, 2020 - - - -
Logic Workshop
CUNY Graduate Center, Room 6417
Friday, February 21, 2:00-3:30pm
Andrey Morozov, Novosibirsk State University
On Σ-preorderings in HF(R)
We prove that ω1 cannot be embedded into any preordering Σ-definable with parameters in the hereditarily finite superstructure over the ordered field of real numbers, HF(R). As corollaries, we obtain characterizations of Σ-presentable ordinals and Gödel constructive sets of kind Lα. It also follows that there are no Σ-presentations for structures of T-, m-, 1-, and tt-degrees over HF(R).
- - - - Other Logic News - - - -
CONFERENCE ANNOUNCEMENT:
The “Sao Paulo School of Advanced Science on Contemporary Logic, Rationality and Information - SPLogIC”, sponsored by FAPESP and promoted by the Centre for Logic, Epistemology and the History of Science (CLE) of the University of Campinas (Unicamp), Brazil, will be held at Unicamp from July 13th to 24th, 2020.
The School celebrates the 90th anniversary of Newton da Costa and aims at: providing an overview of the state-of-art methodology and research on contemporary logic (featuring non-classical logics), rationality, and information.
The program comprises 9 courses and 9 plenary talks delivered in English by experts in each topic, as well as oral presentations (LED Talks) and poster sessions by the students.
Topics to be covered include:
• History and Philosophy of Paraconsistent Logics
• The Australian, Belgian, Brazilian, and Israeli schools on paraconsistency
• Logic and Reasoning, Logic and Information, Logic and Argumentation
• Methodological aspects on interpreting, translating and combining logics
• Logic, Probability and Artificial Intelligence.
The event will select 100 fully-funded participants (50 grantees from all states of Brazil and 50 international grantees). Funding includes airfare, medical insurance, accommodation and meals throughout the two weeks.
Undergraduate students, graduate students and postdoctoral fellows (up to 5 years after completion of the Ph.D) from all countries are encouraged to apply.
Applications are open from January 15th to February 22th, 2020.
More information and Call for Applications at https://splogic.org.
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)
-------- ADMINISTRIVIA --------
To subscribe/unsubscribe to this list, please email your request to jreitz@nylogic.org.
If you have a logic-related event that you would like included in future mailings, please email jreitz@nylogic.org.
Wednesday seminar
Udine Workshop on Singular Cardinals, Udine, Italy, July 6-7, 2020
(KGRC) research seminar talk on WEDNESDAY, February 12
This Week in Logic at CUNY
- - - - Tuesday, Feb 4, 2020 - - - -
- - - - Wednesday, Feb 05, 2020 - - - -
MOPA (Models of Peano Arithmetic)
CUNY Graduate Center, Room 4213.03 (Math Thesis Room)
Wednesday, Feb 5, 6:30-8:00pm
Athar Abdul-Quader, Purchase College
The pentagon saga continues
- - - - Thursday, Feb 06, 2020 - - - -
- - - - Friday, Feb 07, 2020 - - - -
Logic Workshop
CUNY Graduate Center, Room 6417
Friday, Feb 7, 2:00-3:30pm
Victor Selivanov, Institute of Informatics Systems, Novosibirsk
A Q-Wadge hierarchy in quasi-Polish spaces
Next Week in Logic at CUNY:
- - - - Monday, Feb 10, 2020 - - - -
Logic and Metaphysics Workshop
Date: Monday, February 10, 4.15-6.15
Place: Room 7395, CUNY Graduate Center
Melissa Fusco (Columbia).
Title: A Deontic Logic for Two Paradoxes of Deontic Modality
Abstract: In this paper, we take steps towards axiomatizing the two dimensional deontic logic in Fusco (2015), which validates a form of free choice permission (von Wright 1969, Kamp 1973; (1) below) and witnesses the nonentailment known as Ross’s Puzzle (Ross 1941; (2) below).
(1) You may have an apple or a pear ⇒ You may have an apple, and you may have a pear.
(2) You ought to post the letter = ̸⇒ You ought to post the letter or burn it.
Since <>(p or q) = (<>p ∨ <>q) and [ ](p) ⇒ [ ](p ∨ q) are valid in any normal modal logic – including standard deontic logic – the negations of (1)-(2) are entrenched in modal proof systems. To reverse them without explosion will entail excavating the foundations of the propositional tautologies. The resulting system pursues the intuition that classical tautologies involving disjunctions are truths of meaning, rather than propositional necessities. This marks a departure from the commitments the propositional fragment of a modal proof system is standardly taken to embody.
Note: This is joint work with Arc Kocurek (Cornell).
- - - - Tuesday, Feb 11, 2020 - - - -
- - - - Wednesday, Feb 12, 2020 - - - -
The New York City Category Theory Seminar
Department of Computer Science, Department of Mathematics
The Graduate Center of The City University of New York
Speaker: Tai-Danae Bradley, The Graduate Center, CUNY.
Date and Time: Wednesday February 12, 2020, 7:00 - 8:30 PM., Room 6417.
Title: TBA.
Abstract: TBA.
- - - - Thursday, Feb 13, 2020 - - - -
- - - - Friday, Feb 14, 2020 - - - -
- - - - Other Logic News - - - -
- - - - Web Site - - - -
Find us on the web at: nylogic.github.io
(site designed, built & maintained by Victoria Gitman)
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Set theory seminar this week: Assaf Shani
The talk will be held on Friday, February 7 in Fields 210 from 1:30 to 3:00. If you will attend the talk, please register using the following link:
Logic Seminar 12 Feb 2020 17:00 hrs at NUS
Wednesday seminar
Logic Seminar
Asaf Karagila
Newton International Fellow, School of Mathematics, UEA (Norwich)
THE POWER OF POWER SETS OF COUNTABLE UNIONS OF COUNTABLE SETS
Wednesday, February 5.
12:30
IMUB Lecture Room, Facultat de Matemàtiques i Informàtica, UB.
http://www.ub.edu/slb/Seminar.html
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Re: Set Theory Seminar
Eduardo Sealtiel Martínez Mendoza: Teoría PCF e hipótesis del continuo generalizada revisada
Logic Seminar Wed 29 Jan 2020 17:00 hrs at NUS - Talk by Wang Wei
Set Theory Seminar in the Stewart Library this week
Wednesday seminar
(KGRC) research seminar talk on Thursday, January 30
Set theory seminar next week: Henry Yuen
The talk will be held on Friday, January 24 in the Fields Institute from 1:30 to 3:00.
Set theory seminar tomorrow: Spencer Unger
The talk will be held on Friday, January 17 in Huron 1018 from 10:00 to 11:00. If you will attend the talk, please register using the following link: